Question about PE Headhunters

Hi all - do PE headhunters (in the US) that work with people at the associate/lateral associate level (ex. HSP, Amity, Ratio, CPI, Carterpierce) also work with candidates for post-MBA recruiting? 

For context, I am a 2nd year associate leaving my current fund (fund is doing poorly and they arent promoting anyone), I got into some 1 year MBA programs starting in August and wondering if they work with people who are doing their MBA for positions a year out.

Thanks all