I recentally started the AST app process and did some talking with the recruiter as well. Like others stated they do not hire straight into pilot slots. Infact they were very unimpressed with my flying experience from what I was gathering. They said Troopers are issued a C185 just like a highway patrol man is issued a Crown Vic in the lower 48. It all just depends on where you are assigned. Your first year of field training is done in Soldotna, Fairbanks, Palmer, or Bethal. After which point you could be forced to transfer to BFE for your next 2 years. Or you could get lucky and stay in your orginal field training location, but promotion would be much slower. After 5 years of senority, you can not be forced out of your post and into the Bush.
They are very few areas in AK that are accessable by road, which is the reason the AST uses boats, planes, ATVs and snowmobiles. You only receive a 3% pay override for being a qualified pilot. I dont know if the risk is worth the reward.

I would take 10 minutes and talk to a recruiter and see what you think.
Toll Free. 1-877-AK-TROOP (1-877-258-7667)