MHA -> healthcare private equity?

Can people place into healthcare equity out of an MHA program? If not, do the other 3 routes below seem plausible?

1) start MHA program -> summer intern with Healthcare IB -> graduate with MHA -> break into healthcare IBD -> work for a couple of years -> break into healthcare PE after years of healthcare IB experience

2) same as the first one, but instead of healthcare IB, you do healthcare consulting then healthcare equity

3) same as the first and second, but instead of healthcare IB or consulting, you do healthcare administration then healthcare equity