Will I get an email if the IRS accepted my payment plan?

If you applied via Turbotax, I think you get a letter in the mail.

IRS, like Donald Trump, doesn't do e-mail.

If you apply directly online at the IRS web site, you get immediate notification, but it comes from being logged into the secure installment plan web site, and not via email.  If you apply through Turbotax, you get a letter in the mail.