Bladethirst + Enhance Arrows + Arcane Strike?

[Amuny]

First, links;
Bladethirst
Enhance Arrows

Then question:

Could a Level9 Bard / 3 Arcane Archer suddenly have such arrows with an absolutely non-magical bow/arrow at the beginning?
- + 1 from Enhance Arrows Level 1
- Shocking from Enhance Arrows Level 3
- + 1 from Bladethirst
- Frost from Bladethirst
- + 2 damage from Arcane Strike

And then shoot with a plain longbow arrows, without any other feats or ability, something like;
1d8(base) + 2d6 (shock&cold) + 4
per arrow?

And pushing it to the max, what if I take some paladin's or magus levels to get the equivalents abilities?

[Dekalinder]

Well, if you want to be really stingy with the rules, the bow must be at least masterwork otherwise it cannot gain enchantment. Other than that, yes it can. And no, I don't think is OP.

[Amuny]

Dekalinder wrote:

Well, if you want to be really stingy with the rules, the bow must be at least masterwork otherwise it cannot gain enchantment. Other than that, yes it can. And no, I don't think is OP.

I don't think it's OP either, just wondering if those abilities could stack together or not