HiTag is not super common here on the forum, I personally know very little about them.
I think at the end of the day, it will depend on how the system is implemented, Copying HT onto T5577, may be possible, but if it uses challenge and response, or the full UID you may have some issues.
If enrolling a “bring your own” is possible, that might be your best option, but this will require the access admins to be on board.
Alternatively just try it, Grab yourself those HiTag bands and some T5577 test cards and see if you can get it to work.
Sorry I cant be much help, I don’t even own a HiTag to test for you ( Note to self: get HiTag cards 
)
Here is a quote from one of my posts, but if you follow it to that original thread, you may get some more answers.
Good luck