Yes, that happens sometimes.
After Ellie got DHLPP-C and rabies (by the way, no animal of mine will ever get this many the same day again), she threw up, collapsed and went into shock. She was unresponsive and needed emergency care. It was most likely lepto or rabies that did it.
I didn't know of the dangers of lepto at that time and I didn't know that rabies should never be given with any other vaccine.