Paying estimated penalty with tax filing

I opted to pay an underpayment penalty with my tax filing rather than waiting for the IRS to bill me for it. Will the IRS still bill me for it and then apply my payment to it? I want to request for a first time penalty abatement but it looks like I have to wait for the tax notice so I have something to respond to with my request. It does not seem possible to make my request immediately right after my tax filing.