Will having a private equity internship help with traditional PE recruiting?

I have an exploding offer for a PE internship during the school year. It's a smaller shop, though possibly recognizable within the industry. It is unpaid, and my course schedule will be pretty loaded this semester. If I don't take this internship, I'd probably prep for and take the GMAT.

I was wondering if accepting this offer would allow me to have a leg up during PE recruiting. I am going to be an IBD intern at a BB this summer, so if things hopefully work out, I was planning on the traditional 2-year analyst stint in banking.

The internship would also be at a fund that targets mostly the lower middle market in a specific industry; I was hoping to eventually recruit for larger funds, and am not super interested in that industry. However, still definitely would take this offer if it helps with recruiting (seems like a great educational opportunity as well). Thanks y'all - anything would be helpful!