How long are we talking?
I have had them under a car for days and even a couple weeks, but I'm not sure I have had them on for more than that.
I am confident that you are not going to hurt them if it just a car on them, not a larger truck or something.
Keep in mind that if the tire goes flat for whatever reason that you may not be able to move the car as the tire could then contac the floor. What do you do then?
If you get a good set of wheel dollies that cover the whole,bottom of the tire, then you are less likely to have that issue.
Will the spot pressure on the tires from go jacks cause issues over time? Could.