Yes, it can do it. Will it be easy, no.
It sounds to me like you're going to attempt multiplayer and the host will be the server. For very simple stuff, Ajax can do a lot. For tracking player movements, bullets, etc. you're going to need a full blown websockets server. While C3 does have multiplayer built in, my experiences with it have been a lot less than inspiring. And multiplayer servers? That's a huge, huge ball of wax.
If you're new to Construct, I STRONGLY recommend you start with a single player game. Multiplayer servers is a whole field of computer science unto itself.