I studied abroad fall semester of senior year and ended up deciding to take a gap yr, but that was because I decided to take 2 pre reqs a little later and I would have not been able to attend interviews etc.
I would say that nowadays it would be very doable to study abroad during the app process. And if you have a solid app and still have the margin to leave and go study abroad it would set you apart as an applicant and make you seem interesting as well. I would recommend submitting your app and getting it verified before you leave..you will have an advantage in rolling admissions etc the earlier you submit it as well. As long as you have info, prereqs, and letters of rec sorted out then you will have over a month to pick your schools, write your personal statement and essays, and finalize things. After that it’s just a waiting game unless you need to update PTCAS or have an issue. I did my whole app and all school specific questions in 3 days, then took 3 days to get verified. Almost all of the programs are doing virtual interviews this cycle and have been very accommodating, so I imagine it would probably be similar for this upcoming one. Start the process and you’ll probably figure out pretty quick if that’s what you want to do or not, no harm in wading in a bit!
tldr, it’s very doable...If you know you want to go right into PT school and have your stuff all together, then go for it!