Lateral to Career-Track after Finishing Program

I will be joining an MM PE fund with a fixed-term associate program. I like the fund and strategy, and as an IB ASO, don't have any illusions about what I'll be getting into. I know I'll be trading down on hours, responsibilities, and near-term comp, all of which are not an issue.

However, I am a bit concerned about the associate program because the fund expects associates to go to business school. There is a path to career-track, but it's more an exception than the rule. I have no interest in business school both for financial and personal reasons. Not to mention that my resume is probably not competitive for any business school where I could get serious PE looks. Ideally I'd like to secure a career track at this fund, but if I don't, it seems like my best option is to lateral.

How common is it to finish up a program and lateral to a comparable fund for a career-track role? Do MM funds typically hire career-track senior associates? I would prefer to finish up the program before considering lateral moves, but not sure if I should start thinking about this earlier.