You can. But before you do that, I HIGHLY recommend you do some things first.
If you haven't done so already, open up those old tax returns in their respective version of the program, and save them as PDF files. When you save them, elect to save EVERYTHING, and not just those pages required for filing, or just "for your records". Save EVERYTHING to a PDF file. That way, if you need to look at something in the future, or if you get audited, you can open that return in the Acrobat Reader program, and print if necessary.
In addition to the above, I also recommend you print EVERYTHING so that you have a physical hard copy. That could very well save your butt in the future if you should get an audit notification the day after the computer with the PDF copy on it, craps out on you. For people like me with 3 rentals and self-employed, my printouts each year are in excess of a hundred pages. But it's a one time deal each year and I do it.
bottom line is, do not use thumb drives for long term date storage. You're better off using a CD or DVD for that.
I'd save the CD's for at least the last 3 prior years in case you ever need to amend a return, or if you have a computer/drive failure and have to reinstall the program. As for program updates, state program downloads, etc. TurboTax only supports software for the current and prior 3 years.