First, just because turbotax printed vouchers doesn't mean you need to pay them. Turbotax based the vouchers on last year, so if your situation changes, you might owe more or less.
Then, yes, paying as soon as you can will help reduce penalties and interest, but probably not eliminate them.
I recommend that if Turbotax suggest you owe a penalty and wants to include it, you decline that suggestion, and wait for the IRS to bill you. If they do, you can apply for a waiver/abatement. It's harder to apply for an abatement if you already paid a penalty with your tax return.
https://www.irs.gov/payments/penalty-relief-due-to-first-time-abate-or-other-administrative-waiver
