What you described is definitely possible. That CR3032 might not last very long if you're using a XBee transmitter as they tend to soak up a decent amount of current. The XBee has a pretty small form factor and you can use advanced configurations
to set it up to detect button presses instead of just transmitting 9600 BPS serial data.
The XBee modules have an interface you can communicate with, however for the most part they are designed to be transparent from the communication process and make the system act like you're just connecting wire-to-wire.
Here's my intro the XBee Article:http://www.pyroelectro.com/tutorials/xbee_wireless_interface/
It'll take some research to understand how to use the XBee's properly, but without a doubt they can be used for the system you have described.