That's a really interesting point. Ungoliant kind of exists outside the established power structure of the Ainur, considering she came from outside Arda, but was never mentioned as participating in the first music of the Ainur (there's no real established origin for Ungoliant, other than "evil spirit from outside the bounds of Arda"). No matter who you are, being called to fight "unknowable ancient Eldritch spider deity" is a pretty horrifying task, and Melkor was even known to have fear when facing much smaller enemies.

One interesting point is how much emphasis Tolkien puts on Ungoliant's powers being focused around darkness and "unlight". Balrogs, being spirits of fire, seem like a natural enemy to a creature of pure darkness, so that might have boosted their comparative power against Ungoliant despite their low numbers.

Another thing to consider is that Melkor was never known to show understanding or mercy to his servants who failed him. I would have to think that any balrog who failed to come to his aid would have been killed (or worse as you postulate) as soon as Morgoth was freed.