Does PE/HF firms recruit directly from MBA schools ?

Hi everyone,

I have received a FT offer at a top 5 bank in NY ( think GS, JP, CS, BAML) and will start working as a first year IB analyst this summer. A lot of people in my shoes are already thinking about PE/HF recruiting. I am not 100% sure about PE yet and leaning toward working in IB for 2 years then do something else. Right now, I want to join the U.S military after my 2 years in IB to pay my dues to the country, then go to business school.

My question is, can I do undergrad-> IB->Military->PE/HF or undergrad-> IB->Military->MBA->PE/HF or do I have to do the traditional IB->military->MBA->IB->PE/HF ?

Any advice is appreciated