The "transmitter" should just be thought of as a wire. What you put into it, comes out of the receiver. That's all. The channels, house codes, and all the rest of that comes from the encoder on these remotes. But, since you are using the arduino, YOU are the encoder and have complete control over all of that. So, no... you would use only one 315Mhz module for all 315Mhz remotes, one 350MHz module for all 350Mhz remotes, etc... Your code handles the channels, housecodes, etc...
The rfswitch library I link you to handles all of that. You send whatever you want over the RF module.
There is nothing locking the actual radio module to specific channels, etc... all of that is done in the encoder. Check out the datasheets for a PT2262 attached. Nearly all of these remotes use this or some clone of this.
PT2262.pdf (454 KB)