Should I take an unpaid PE internship? - incoming IBD analyst

There's a significant part of me that wants to say never work unpaid, but it seems you are going to headed somewhere else afterward that will give you decent money, so I'll balk on my normal adage in your case. 

Ultimately, if you're looking mostly for the experience, I would say go with whatever will maximize your learning experience and lead to the best possible recommendations for your next steps. I think if you feel the experience alone is worth it, then do it. I've been in your spot with clinical research in the past and thought the experience was worth, but if I could do it again, I'd do it for money. 

Also, since it's only ~15 hours/week average, that's like 3hrs/day for 5 days/week which is not a killer, I think that you're not overcommitting yourself either, which is honestly a good thing here. 

Go for it, you have a bright future ahead, and a learning experience you don't have to pay for.