i’ve used and abused caa a lot to tow cars. they only tow if your car is “broken down” but as long as they think it is then you’re fine, just make sure they think it’s something major that’s wrong otherwise they’ll want to try to boost your battery first. the plates have to have a valid sticker on them and i’ve only had one guy check to see if the plates match the car (out of about 20-25 tows between my friends and i), luckily the plates matched that time.
don’t act sketchy otherwise they might try to check up on the situation (i.e. see if plates match the car, etc)
good luck.