Lost phone and requested factory reset through google, will it still work if disconnected?

[AC Question]

So I lost my phone at school on Tuesday. I went on to google account when I got home and set up a password lock on the phone, since I only had a swipe lock on. Which means they have/ had access to all my information, pictures etc. Now, I went on to google and requested "erase" option. My phone is currently still connected, however, whomever has it, turned it off. My question is, will the factory reset still happen, once they power it on? I'm not sure if I still leave my service connected until they turn it on to ensure it will happen. Please help. I don't want them to access my stuff.