I think it depends on the terms of your TDY, like how long are you TDY?
I say this because back when I was in the military I was assigned to a unit in HI (HI is the only state I have never set foot in) and was posted TDY elsewhere...for 18 months. Never once saw the Command in HI even though all my records say I was assigned to HI for the full 18 month tour.
Residence, is residence, Work is work, If you are there long enough (the state you are TDY to, that could be 30 days, could be 90..depends on the state law). I would say that if the state law says you are to be considered a resident because of the length of the work assignment, and you will have documentation to show that (utility bills, phone bills etc). Personally, I do not think you would be turned down.