Not having an agreement with FOM may impact the FIA's evaluation of the viability of a team.
Which is, after all, one of the main concerns has for new teams. That and technical capabilities.
Sorry, but no.
FIA Phase 2 of the application process, which Andretti passed and the other three applicants failed, is based on 'sporting, technical, and financial analysis'.
FOM has no competency to do sporting or technical analysis. FOM might have competency to do financial analysis (which would cover the applicant's own financial viability, not its commercial impact on the Commercial Rights Holder or the other teams), but there is no reason to think that FOM would understand more about the financial viability of a racing team than the FIA, with its decades of experience in precisely that subject area, would do.
It is possible that FOM has a contractual right to an ultimate veto, but that would not be because it is in a position to know more about the FIA's criteria than the FIA itself will do. FOM had its own criteria, which were purely about its own, and the existing teams', financial returns.