Applying to MBB Full-time after Internship Rejection

Hi!

I attend a target university for MBB on the east coast, and applied + made it to first round interviews at McKinsey and Bain. However, I didn't prepare at all for either interview, as I was caught in a midterm exams, and honestly wasn't motivated, since I wasn't sure if consulting was the path for me. I went to the interview mainly for experience. Ended up getting a rejection (obviously).

It's been a few months now, and I've managed to land a 2nd tier consulting internship (ZS) for the summer, but really would like to be at MBB full-time. Do you think the fact that I was rejected for an internship will impact my FT chances--would they decline to even interview me? I'll be working in consulting this summer + will, in addition, be spending several hours a week prepping.

Would love to hear any thoughts.