how do I access a prior return on desktop without updating?

The updates that TurboTax is referring to are software updates.  

None of the information in your return will be affected.

You can continue with the updates without any issues.

Did you save a pdf of your return before?  You should always save the pdf right after you file and it was accepted.  Then if you open the .tax file later and it does updates you can compare it to the pdf to see if anything happen to change.  

For Windows,  the first thing I do after installing the program and it does the first update is turn off the updates.  I  go up to Online-Updater Preferences and check Ask me before getting updates.   Then I can control them.