Yes. In fact, this is a good example of why they sell wireless-enabled printers.
First of all, if you connect any printer to a network router (either by network cable or by wireless) and NOT to a computer, that printer becomes a network resource available to any and all computers on the network. So no matter which computer, or where it is located, the computers on the network can be set up to use that printer as an output device. (Depending on what the printer can do, it may function as a printer, a scanner, and / or a FAX sender-receiver for ANY computer on the network.) For example, I have a colour laser printer on our home network that can be used by four computers - two in the family room, one in my son's bedroom, and one in the living room.
Secondly, whether you use a network or not, a wireless printer is designed to be used EITHER with a wired or wireless connection to your computer. A very common system, though, is what you have: the printer is connected to your home network via a wireless connection to your router. From then on no computer cares or needs to know how that connection was done - the printer is simply available to any computer on the network. Each computer simply has to be set up to use that printer. Among other things, that means that when the printer is "installed" on each computer, it is told that the printer is not connected directly to a port, but is on the network. It does not need to be told that the network uses a wireless connection to reach the printer. And yes, the printer can be placed anywhere you like, as long as the wireless signals from the router can reach it.