After I filed my taxes, I received a W2 for a small amount of income that I had forgotten about. Do I need to file an amendment if it doesn't change the outcome?

[WillK]

Yes, you need to file an amended return since the IRS will have a copy of that W-2 and will be looking for it on your return. You should not try to amend your return until it has been fully processed and you have received your refund or your payment has cleared.

Amended returns do not “catch up” to your original return and replace them; they are processed as two separate returns.  
Amended returns have to be printed and filed by mail.  It can take the IRS up to 12 weeks or longer to process them.   If you are due a larger refund than on your original return, your amended return should only show the difference and you will receive a separate check for it.  If you owe money on your amended return, it will show only the new amount owed, you will have to mail a check with the return. Click here for the TurboTax FAQ on amending your return: https://ttlc.intuit.com/replies/3288565