For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Vincent Mercado
I guess it depends on how much significance the people placed on the veil.
If they thought they could simply replace the veil, I'm sure they will still continue to use the temple.
If they thought the tearing of the veil signified the destruction of the temple, in the spiritual sense, then they will stop using it.
For me, I think the temple was already useless because the ark was not in it, even if the veil was intact. After Jeremiah took the ark away, the Shekinah cloud never returned to the temple.