Well, no, this isn’t exactly how it works. When on ADT, they will cover the cost of your housing for whatever away rotation you are on. When I used my 3rd year ADT for my first 4th year away rotation, it was in San Diego so they covered my entire month long stay at the navy lodge, paid for a rental car for 1 month, and paid for my flights to/from San Diego. In addition to that, I got my full active duty pay instead of my Hpsp stipend.
If you use your ADT at a different time, you’ll get the increased pay by being active duty but you’ll miss out on the hotel/rental car/plane costs and will have to front those yourself.
I did 3 away rotations. 2 were covered by ADT orders (I saved my 3rd year ADT and used it before Oct 1st of my 4th year, and then I used my 4th year one after Oct 1st). I had to pay for last away rotation out of pocket. The out of pocket one I was able to drive to (so no flights or rental car needed), but I had to pay a USUHS student for rent to use his house for my 1 month rotation.
But for ODS, you have to save an ADT for that. You can’t go to ODS and not be on active orders. So you’ll have to plan for that.