Received a corrected W-2 after filing taxes and the only correction was the withheld amount for Social Security - does this require an amendment for either submission?

Yes, you should file an amended return since a dollar amount changed on the W-2. If you already filed your return you will need to wait to see if it was rejected or accepted. If they were rejected you are able to login to your return to fix what you need to fix and fix the errors that caused the rejection and refile the return. If your returns were accepted, then you will need to file an amended return. You should not try to amend your return until the original return 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. You can check the status of your amended return by clicking here: https://www.irs.gov/filing/individuals/amended-returns-form-1040-x-/wheres-my-amended-return-1

We can't say for certain how this will affect your refund. However, you will want to add your corrected W-2 at some point.

Once you've filed your tax return, do not make any changes until the IRS either accepts or rejects your return.

If accepted, wait until the IRS issues your refund (if applicable), then you will need to amend your return.  The following TurboTax FAQ can guide you when you are ready to amend:  How do I amend my 2019 TurboTax Online return? - Community

If rejected, you can sign into your TurboTax Online account and fix what caused the rejection.  At this time, you can also add your corrected W-2.  Refer to the following FAQ for assistance:  How do I fix a rejected return? - Community