the arduino can handle a max of 5 volts dc (ok 5 + like .5 but its a 5 volt system) SO if its 5v dc yea you could hook it up to a digital pin, its not very likely that the doorbell actually runs on 5v dc (but hey you never know with modern things)
as far as just using the button and basically using the doorbell box as a enclosure you would hook it up to any digital pin just like any other button in the example
http://arduino.cc/en/Tutorial/Button
taking length and guage of wire you will loose voltage in the trip, but it still should be enough to perform its function.
Sorry for all the questions and confusion, but I really appreciate the help.
dont be, and your welcome