I don't think they will. When you get back, though, they would probably like to get the ball rolling. It does depend on if they are hiring and who else is in the running for it. I think an agency would love to get a person with some LE experience and military, but there are a lot of hiring freezes throughout the country. Good luck.

I spent a couple years in Central Florida. If you don't mind me asking, where are you looking to go?

Nothing wrong with having them send you the application packet so you can have that part of the hiring process ready to go when you get back home.  But I think you would have to be available to the agency for the written exam, fitness indicator testing or whatever else the agency may have for prescreen or initial qualification requirements. Followed by the BI once those hurdles are cleared. 

My guess,and this is strictly a guess, is that if your deployment is scheduled it end in 2 or so months, go ahead and apply.  It sounds like you ae trying for a lateral transfer, and even though it is for an entry level position, they may do it as a lateral transfer.