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What exactly are you trying to get out of the build? If you only dip ZAM, you'll still need a good dex to qualify for archery feats, so the wis to hit is wasted. If you stay in longer to get more feats and WIS to hit, you are severely stunting you cleric casting.
I think in most cases, the concept works better as a single class cleric of Erastil.
If you ZAM 3 then you're 3 levels behind on your cleric casting and your casting is quite poor.
If you don't care about casting then there's not much of a reason to go into cleric. But if you don't care about casting then yeah, dip to your hearts content. Mundane fighting doesn't really care how much you dip.
Nope still a poor caster, if you're 13th level and only have 10 caster levels you're a poor caster for your level. Comparatively you're looking at only having 5th level spells when a lv13 caster would have 7th level spells.
Is it an archer that is also a lv10 cleric? Yes. Now is it good enough for what you want? I don't know. It's up to you to decide what is "good enough"
Also, something to realize, what do you plan on doing for one of your turns at lv13? Do you plan on casting a spell most rounds of combat? If so then your archery levels are wasted. Full attacking with a bow? Well then you do have spells as a back up for out of combat stuff. But you can't do both and so you need to decide what your main deal is.
*The General rule on the Forums is "Never give up caster levels" so anything that does so will be seen as a less optimal choice.
Your save DC for your channel will be lower than a full cleric.
You're more mad now, wanting str, wis, con and now charsima
If you're going with offensive spells you don't want to dip out. If you're wanting buffs then it's okay. But why not just go Warpriest? gets you swift action spellcasting for buffing and lots of bonus feats.
Will your proposed character be viable? Yes, probably will work pretty well. Is it the best choices? no. So the issue is "how good do you want to be" and "does this mean those qualifications?"
Your ZAM dip is getting you wis to accuracy and rapid shot for free if you use flurry.
You could just go warpriest and have all the feats you need about as fast and you'll be full caster level with swift action buffing.
If you're happy with it then go with it. I hope you don't die being so close to enemies and having low AC and HP.
Warpriest is a full CL class. If you were just Warpriest then you'd be at full CL.
The thing about only going Zen Archer 3 is that you never get more flurry of blows attacks, but you also don't get to use Rapid Shot or Manyshot. So an archer Cleric can do +2 attacks per round by level 9 with Rapid Shot and Manyshot, and a Zen Archer can eventually do +2-3 additional attacks per round by 8 through flurry and ki. But Zen Archer 3/ Cleric will only ever get +1 attack from basic flurry.
It seems you were sure of what the answer was for you before you asked the question. Makes me wonder why you bothered to ask it at all.
However, I am sure that everyone is happy that you are satisfied with the character you are making.
I agree with the others that a single class ZAM will be a better archer, and a single class cleric will be a better cleric, and your character will be less effective at either. I also think a warpriest would do a much better job of straddling the line between the two.
This is certainly a playable character though and something a person could enjoy, just not optimal.
I should check this because you sound adamant, but a think Warpriests have 6 levels of casting, not the typical 9 levels a full caster gets.
+5(wis) +3(DF&FV) + 4(flurry) -2(DA) +2Weapon Enh
+Ki attack= +12/+12/+12/+7 for (1d8+3(DF)+4(DA)+2(WE)+1(STR))
...plus you could not make this build by 7th level with a Warpriest.
It's not a 9th level caster. But it does get full caster level.
then, your build doens't have a ki pool to be able to make the extra ki attack, You'd need a fourth level of monk to do that.
WP Human
14/17+2+1+2/14/7/14/7
1 PBS, Precise shot, weapon focus
3 Rapid Shot, deadly aim
5 free
6 many shot
7 free
1st round
+5bab +6dex +3DF-2DA-2RS+1wf+2weapon = +13(double hit)/+13/+8 for 1d8+11 (1d8+3(DF)+4(DA)+2(WE)+2(STR))
2nd round same +1 from sacred weapon to attack and damge.
So I shoot more accurately for more damage on the first round than you do on the second round. I don't have to worry about moving at all (which you do to stay near front line, so if your front line moved up you'd need to move to stay with them and then you couldn't channel and buff that round)
And then I get better on round 2, while you're finally attacking round 2.
My build gets better next lv as the sacred weapon goes to +2 and then again at lv9 when DF goes up. It'll take you 3 levels to increase your DF and you don't have my sacred weapon scaling.
Plus if I went arsenal chaplain then I'd have another +1 to attack and damage from weapon training that would also go up at lv9.
Also at lv7 I have 3rd level cleric spells and you at "4th" level only have 2nd level cleric spells. So I'm the better caster too.
other thing to think about is building around WIS to Ranged, since you don't get it at 1st level.
yet the abilities/bonus feats you get are all ranged focused, and you should be putting normal feats into ranged as well.
for a pure ZA those first levels are tough if they want to build for WIS, either they prioritize WIS and STR
in order to maximally optimize later level performance, and default to mediocre melee until getting WIS to Ranged,
(or at least "switch hit" for ranged flurry at crappy to-hit, and switch to melee for more to-hit/dmg when enemy closes)
or they split point buy into WIS/DEX/STR for higher AC but less offensive optimization (STR dmg, WIS attack),
which undercuts the value of WIS to Ranged if in fact it ends up being less offensively potent than DEX build.
(if you're OK with that, and just want synergy with other defensive benefits, OK but be clear on that)
your build also wants to have CHA moderately high... as well as demands on STR for dmg, CON for HP... making it even tougher.
for that reason, only ZA dip I've played (with Inquisitor) in fact only dipped 1 level in ZA never gaining WIS to hit.
basically i was taking it for huge amount of bonus feats (with flurry effectively rapid fire with full BAB) and good saves.
not progressing flurry (which your proposed 4 level dip doesn't do either) means in some ways it's (eventually) worse than
taking rapid fire + manyshot, although with full BAB equivalent and Perfect Strike it isn't clear cut.
But really it is worthwhile for 1) coming online quick 2) leaving your feats free 3) great saves.
While it maybe wasn't maximally optimized offensively in later levels, with Inquisitor abilities (1 level delayed only),
it still worked "good enough" since Bane/Judgement * Archer Full Attacks is potent enough without Manyshot.
(I actually leveraged WIS further by taking Stunning Fist via Feat which the 1 Monk level gave me extra usage of)
I think that could potentially work well with Cleric too, with Cleric buffs (just 1 level delayed)
keeping up your offensive relevance, enough to compensate the lack of Manyshot for the most part
(and having much broader utility outside of archery as well)
You should seriously consider Warpriest though.