A wellness check is when you have the police go check if he's doing alright. Unless you think he is suicidal I would recommend not doing a wellness check. I've had family do this to me and I don't like it. When I get depressed I just what to be left alone, having the police come to my house would likely cause me a panic attack.

If he asks you to leave him alone, then respect that, tell him ok, I'll be here when you're ready, and walk away. Are you still at his parents? Since he doesn't have a phone, and presumably a car, I would go check in with him again. Maybe leave your phone with him and take his phone so you can charge it up.