I have not read any restictions pertaining to tax payments although that is a component of payroll. The EDIL and PPP are not supposed to cross-mingle when it comes to spending I have read that. I would research to see if there are some payroll tax deferrments available to you. I you use a payroll company like Paychex or ADP I would contact them or your CPA to clarify. Wish I could be of more help.
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I see no reason not to pay quarterly taxes (I assume that you are a sole proprietor or independent contractor) if you are paying them to yourself first. That is "your pay." If it is not okay, the worst case scenario seems to be that you will have to pay back the loan at 1% for paying income taxes that you owed anyway. I don't see much downside.