No. A user does not have to enter any product serial number in order to file a return. I don't know if TurboTax tracks it by another method, but there is nothing to enter in that regard at the user level.
TurboTax does keep track of the number of efiles. With the desktop product, one can prepare multiple Federal returns, but there is a limit of 5 Federal efiles (IRS rule.)
There are a couple of reasons why you might need a serial number:
When using TurboTax Desktop (CD), in the event that you need to upgrade the product (like, if you accidentally purchased the wrong version, i.e. you purchased Basic, but need Deluxe) or if you are going to e-file your state return, you’ll see a "Let's Complete Your Purchase Online" screen. See picture below:
When you click continue, if for any reason, you’re unable to complete the purchase on your own, and click on the “We can help you here.” link…
… the next screen – “Purchase By Phone” will have the number to call along with a serial number to provide the support person. See picture below:
The other reason you might need to locate a serial number is if you purchased a CD and then realized your computer/laptop doesn’t have a CD drive. In this case what you’ll need to do is call customer support and provide the 6 digit CD ASM number (sometimes also referred to as the serial number) from the front of your CD to verify your purchase. No other codes from the box will work. You can view the full instructions here:
Yes, technically there is a 6 digit ASMD number on the inner ring of the CD, which is difficult to see. However, the customer is never in need for it. All of the examples you are giving is where the agent needs a software- processed serial number in order to provide a system-processed confirmation number in order to add the e-file option. Those serial numbers change every time you click on "we can help you here."
It is the ACTIVATION NUMBER which is in regular need by the customer.