I am a current Fulbrighter in Germany who applied MD/PhD this cycle and interviewed while abroad. I met a lot of people along the way who were doing the same thing, and although it's possible, I would never recommend it. Like
@Lucca said, you have to have a lot of money to fly back and forth. You're probably looking at a minimum of one or two international trips if you're lucky enough to pool your interviews together, and most programs offer a minimal amount of assistance when it comes to travel. Alternatively, I've met people who have flown back and forth for each interview, and they are usually students from the UK on a Gates or Marshall scholarship (apparently UK programs aren't super flexible?).
I'll speak from personal experience.
I flew back and forth from Europe twice (first in late October for 4 weeks and again in early January for about 3 weeks) and I had a slew of interviews each time (6 and 8 respectively). Interviewing back to back was annoying, flying from state to state was exhausting, and honestly, I felt really bad for having left my project for so long twice. I'm assuming that you're a competitive applicant considering your plans, but I've also been surprised by Gates scholars who didn't even get interview offers at certain programs. That said, I suggest that you apply broadly, so that you have more flexibility when it comes to interview scheduling. Do you have to go on 14 interviews? No. It just so happened that my first round of interview offers were from really great schools, then my second round of interviews a month later were from impressively prestigious schools. I'm sort of thankful that it happened that way, because had it happened the other way around or all at once, I wouldn't have considered going to the first set of schools, and I place them all on equal footing now. Plus, you never know where you'll actually get in. Most schools were very flexible with me in terms of dates, but some schools were not or couldn't be. Johns Hopkins and UCSF actually went so far as to rearrange my interview schedule for me, but I would advise one to be cautious with these rearrangement offers. I personally think that, depending on the circumstance, it could work against you and show that you're not very invested in them as a school vs whatever activity you chose over them. I had to forego interviewing with Emory because they only offered me an interview in December, and I had to forego interviewing at UCLA because their interview date conflicted with Columbia's. In addition, I couldn't have foreseen that I would not even get an interview at places like UPenn, UCSD, or even Drexel. I personally think that applying very broadly (~20 schools that you would actually go to) helps students who are abroad and have less scheduling flexibility, but considering the randomness of this entire process, it may not even matter that much. That said, there may also be a benefit to applying to a small number of schools and making every effort to attend the interviews you're given. You save money at the application stage, you shell it out again for flights, but you waste less time. Your program would probably also prefer you leaving once or twice for 3 or 4 days at a time, versus what I did (still not sure how I got away with it), so consider that if you don't want to piss off your PI
😉. Lastly, emailing schools to say that you're in the States and you were wondering if they were thinking about giving you an interview offer was largely (actually completely) unsuccessful for me. I've heard success stories, but I think you just have to play things by ear.
I am now at the stage where I'm done with all my interviews, I'm waiting to hear back from a few schools of interest, I've been waitlisted here and there, but I thankfully have an acceptance that I am content with.
Now that I've been offered a chance to go to Second Look, I'm faced with the decision of asking for even more time off, or making the decision from abroad. I initially planned to make the decision abroad due to the fact that that I've already spent a lot of time away from my project/program, however, I've heard many students say that Second Look strongly influenced their decision to go to a certain school, so I'm trying not to minimize its significance. I've heard of many students who simply don't tell their program coordinators when they leave the country for interviews (I'm speaking specifically for Fulbrighters from my country...

LOL). To put it plainly, I simply don't have the guts for that. Nevertheless, I wouldn't advise any student to make an 8-year decision in haste. If what
@Lucca said about the timeline of UK programs is correct, then you actually have a wonderful opportunity to go abroad, come back, and interview in peace. I wish that I had that option, or that I knew what it would be like to interview from abroad before even applying to the Fulbright. I don't regret my decision at all, but I really didn't think things through until the summer before departure as I was applying. Also, life happened to me and I ended up applying "late," meaning that I submitted my primary late-July and worked on secondaries from August to September (probably a bit of October too...I looked up the questions online, but a lot of my secondaries came as I was flying into Germany, I experienced a lot of problems with my internet connection, was jetlagged, and busy with orientation and lab work).
All in all, go abroad, but be aware of the multi-faceted risks that are involved, especially in terms of financial impact. I just realized that you may not even care for my answer since I'm not on a UK scholarship right now, but I definitely want to help any student who is reading this post, thinking about going abroad, and wants to apply to MD/PhD programs at the same time.