I would say yes, as long as the Y has not made any offsetting membership arrangements, like giving the person some unpaid months at the end of the term, or provided some other benefit.
In general, membership fees to a deductible organization are deductible to the extent they are more than the value of the benefits of membership. If the Y membership pays for access to health and fitness facilities at what would be a fair market rate (at least roughly speaking) and access is not allowed due to no fault of the member, then those part of the dues should be deductible. (This is different than if the facility is open and the member chooses not to go. The facility would need to be closed on its own decision or state order with no refunds being given.)
