They'll likely conduct a retest first. If still fail, I believe
you're allowed to POP but designated as "Attended BMT" rather than
as "Passed BMT." Presuming you've fulfilled the other criteria, of
course (fieldcamp, basic trainfire, 75% attendance).
It's correct that fitness results are more for command schools.
BMTC's purpose, other than teaching basic soldiering, is to
identify future commanders.
IPPT failures are usually "marked" after being posted to the unit,
though. They typically tio extra PT cuz the overall IPPT results
count in the Best Unit competition, & every CO won't want a low
score affecting his promotional prospects.