I am an Optimum customer (business and home), and you can do what you're trying to do. However, there are some challenges.
If the camera is behind a firewall, you can create a persistent VPN tunnel from one to the other (assuming both FW can create tunnels).
Your cameras would probably be able to get onto Optimum, but you're screwed with the authentication unless you register the devices with Optimum. This can be done via the web interface on your account or when the device joins the network. I am not aware of any camera that supports web-based authentication like what Optimum requires, so that might be a deal breaker. You'd need to be able to get the devices onto the network and manage that re-authentication somehow. Optimum designed the WiFi public network to prevent people from hopping onto it and consuming a ton of bandwidth, so assume you'll probably get throttled and disconnected after a certain amount of time. That's by design.
I'd also suggest going to http://www.dslreports.com/forum/ool and asking the question there. You'll get some answers to your question, and of course you'll attract some trolls. But for the most part, you'll get the best Optimum-specific answers to your questions regarding their service. OOL resources regularly read the forums, and sometimes there's a chance you'll get a PM from one.