Probably not. Growing up, a kid I went to school with had the philosophy of "always assume that your parents can and do spy on you all the time in ways you can't detect." Overblown maybe, but he never got in trouble for about, so there's that. If you're afraid of the government - which you should be, especially when protesting - it's better to be safe than sorry. Leave it home. Get a burner phone if you need one.
Damn I haven't thought of that kid in like 20 years. I wonder if he ended up a normal adult or not.