Yes, that depends on what the GM has in mind tough.
If you are using the Advanced Player Guide, then a party with Paladin, Cleric, Inquisitor and Oracle is actually pretty good against most of the stuff you can trow at it.
We are 5th level and we have a ranger, iquisitor, ftr1/rogue4, and ftr1/alchemist4. Though the alchemist is fairly different from a wizard there are some similarities, I'll admit, but we generally rule in combat. So it's definately doable.
Depends on the game, kingmaker for example can be played without a magic user very easily.
Sure they can survive, (arcane)magic users do not have a vital role to play they are versatile support. A haste spell is useful but a cleric can do something similar with a spell from APG (4th lvl), SoD effects are win or lose anyway, a rogue might get more appreciation in that kind of party.
I'd propose adding an evangelist archetype if you do not already have a bard, possibly making the other cleric a crusader archetype or paladin hospitalizer for plenty of healing.
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You don't have much in the way of battlefield control; anytime "swing" isn't the answer you'll have trouble. Saves are also non-exciting, especially in the will dept. You should do fair early and run into problems later; to the level that the GM may have to modify encounters so you can survive.
Edit: was responding on Remco. Yeah, there are plenty of parties with no dedicated wizard. Especially if you have a Druid and cleric (or oracle) you won't even notice... you just need a battlefield controller (and ideally buffer). There is now a divine haste, and Druids have lots of solid control options.