Dartmouth Tuck: HF / IM Jobs. Possible?

I am in the process of applying to R2 for top MBA programs, specifically Chicago Booth, Columbia, Dartmouth Tuck, and Cornell Johnson. I am confident in my ability to get into Cornell, 50/50 on Tuck, but am 99% sure I will not get into Booth/Columbia. Combination of "weak" GPA and GMAT and non-URM (aka white) status. Won't go into it here.

Currently, I am an associate at PE-style investment firm, previously did 2 years in MM IB in the East Coast. We do mostly MM buyouts but also have a small ~$100M concentrated public equity portfolio.

Why MBA? I am looking to get more non-finance exposure, want to add more panache through my resume (did UG at an East Coast state school), want to tap into an extensive MBA network, and frankly take my foot off the pedal a tad for 2 years.

My near-term dream goal is to work for a L/S fund for an summer internship and for 2-3 years post MBA, ultimately transitioning to a long-only after that. I know Tuck is very strong with the long-onlys in Boston, not sure about Cornell's buy-side recruitment so color would be appreciated.

My question is two fold: 1) Are there any L/S funds that recruit or have recruited at Tuck/Cornell? 2) Given prior experience and a little networking on my end, is my goal a bit far fetched?

Secondary, and more realistic, goal is long-only IM like Vanguard, Fidelity, Cap Group, Wellington, etc.

All insight/advice/feedback is appreciated. Cheers!