No longer relevant

How strong are your networks? Are you confident you can get interviews for the roles you really want with a 3.4 and the date limitations? If so, I'd do the study abroad program because studying abroad is lots of fun. If you're not sure you can rely on your networks, I'd stay - partly to raise the GPA, but more importantly to network more and try and get in that way. Of course if you're thrilled about returning to your previous employer and decide you want to work in that industry it becomes a no-brainer.

As an aside, is there a chance you could cut the study abroad program short by a little while (while still getting full credit) to return in time for internships? While you may be lucky enough to get an internship at a place with two intakes and consequently one that starts later may suit you, I wouldn't want to (and I don't know if you're allowed to) miss training etc. I ask because I personally studied abroad and it was going to conflict with the start of my SA, so before I went I spoke to the destination school and professors in classes I was taking and they allowed me to take finals early and leave ~2 weeks before finals even started to get home in time for my SA stint.

Is your study abroad university well regarded? If it isn't, stay where you are and just study as hard as you possibly can.

I have to say that while exchange programs are fun, it comes with a pretty hefty price tag and opportunity costs. All you're going to be doing is travelling every weekend and/or drinking. You can do that with a friend over the summer (say when you land your dream job) without having to pay for all the tuition/boarding fees. If the school you're going to is a target school though it may be worth it (assuming it's in an English speaking country), because I've had friends land BB/boutique internships though the school's recruiting events. If it's non-English speaking you can probably forget about it.

Having both interned and done an exchange abroad, I can tell you that no interviewer was interested in my exchange -- which was at a strong target school in Europe -- while most asked about my international experiences by referring to the internship. Unless you ended up interviewing for your dream job with an MD who went to the same exchange school you wanted to go to, I think you might feel more comfortable knowing that you tried your best to boost your GPA before recruiting.