Yes and no. Your isp will have to authorize your connection to obtain more than one IP address. Not knowing where you are from, I have no idea if your isp would, likely there would be additional charge if available. (In the USA typical home connections do not have this option, commercial customers likely have more options.)
The router will allow you to run your own private network. It will assign local IP addresses to your computers, and share a single external internet IP address among all devices connected to the network.