Allison,
I'm not really sure why you would want to buy a multi-engine airplane for that reason. First of all, a Seneca is a fairly high-end, expensive multi-engine airplane to use for flight training.
The costs to rent it may be more than multi-engine students want to pay. FlightSafety Academy uses Seminoles and AriBen Aviator uses the Duchess. I did all my training and instructing in the Duchess. I hope you get a chance to talk to a flight school or FBO and explore your options.
One of my biggest concerns, besides maintenance, insurance, etc., would be whether or not the flight school could keep it flying for you. My next biggest concern would be re-selling the airplane at a later date.
Good luck though! I hope you can make it work out for you! I've known several students that had their own airplanes for flight training and it worked for them...granted they were very well off to begin with.
Jeffrey