Might the SpaceX Roadster intercept any ongoing surveys? There are star survey telescopes in space, and on Earth. I don't really know how to begin to know where they will all be looking for the next few months. On the off-chance that someone does, or can suggest how to find out in a systematic way, I thought I would ask here.

These is JPL's Horizons predictions for the Roadster spacecraft in its heliocentric orbit. They are based on both the last state vector readings from the spacecraft itself plus several optical sightings my medium sized telescopes.

While the car is fairly small, it's still attached to the white, 2nd stage rocket body, so it continues to reflect a bit of light. You can read more and see some astronomical photos in this answer and read this answer for info.
Well I can't give a mathematically based answer. I can only tell that some man-made objects were recorded by sky surveys. E.g. the Rosetta spacecraft was marked as a newly found asteroid by the Catalina Sky survey although the error was corrected quite quickly.
Rosetta made an earth flyby at this time so it was pretty close.

The SpaceX Tesla will probably not come close to earth for quite a time and as such it probably won't show up in any survey.