Tens of billions? No, it wouldn't make a difference, and I think it's highly debatable that those tens of billions would be better off in the hands of the fed. I imagine the people actually giving away billions of dollars don't feel that it would be.
The 2019 federal budget was $4.407 trillion. let's say we're talking about $20B in voluntary tax overpayment (good luck with that!), which would represent .004914% of the budget. That would pay about 3% of the interest on US debt in the last year. It would change nothing.
However, increase the marginal tax rate and you're talking about real money. Maybe in the meantime we can spend a little less on the military, but that's a tough sell too.