Probably froze the evaporator coil causing some leakage. How do you know they broke the duct? Sounds like you have maintenance issues as opposed to tenant issues. It falls on landlord to take care of his equipment not the tennant unless its in the lease. Sounds to me like you are trying to charge them for the problem.

The answer to your question is sure it could have caused the problem.........( the condensation due to the broken duct work). But I am more curious about why, or how the tenants would have broke the ductwork in the crawl space.

ductwork in crawlspace often comes apart due to
poorly sealed & strapped ducts.
gravity is the another factor.

"gravity is the another factor."

Damn you Mr. Newton.