Getting into an MFM fellowship will involve a combination of various factors including strong letters of recommendation, research experience, and good impression on the interview. Although a "big time" program is not a requirement nor a sole factor, it can potentially be advantageous as the letter of recommendations would likely come from well known individuals in the MFM field and the applicant would potentially enjoy "networking" opportunities during SMFM and AIUM meetings as a resident.
Best of luck!