Hypothetically, probably.  But the taxpayer should then contact the state unemployment department and tell them they need to repay some of the unemployment they received because they actually DID have income (sick pay via Form 7202) for that week.

If you can document the weeks they did not get PUA, and that these dates qualify for Leave, sure. In MT, the PUA skipped the final 5 weeks of the year, for instance. Otherwise, they are asked if they got any income that week. Here is the MT question and answer:

"Am I eligible for PUA benefits if I am receiving paid sick leave, paid time off, or other paid leave?

It depends. If you are receiving a partial payment for sick leave, you may be eligible for a reduced Weekly Benefit Amount. You must report your paid leave as income or wages when filing your weekly payment request. If your paid leave is greater than your Weekly Benefit Amount, you will not be eligible for benefits"