I'm on a different network than my participants. Will they still be able to connect?

Yes. This requires the host PC to have cloud connectivity and for participants to be connected to the Internet. You can check if someone is connected via cloud or WiFi by clicking the participant manager icon in the session control bar.

You will then see the participants listed.  Participants connected via Wi-Fi will have a wireless icon (e.g. Participant 1, below) and participants who are connected via the cloud will have a cloud symbol (e.g. Participant 2, below).