96 Grand Am SE Heater Core symptons?

I have a 96 Grand Am SE. It started running a little hot, and when I parked coolent was leaking mid engine compartment. I also noticed fan was not coming on after was warm. I ran a jumper from the fan to battery it did come on. I took to GM dealer and told him above info. There diagnosis replace heater core, gave me a estimate of $1160.00. I called part store said it was a $26.99 part. After reading the difficulty of this job I have decided to bypass heater core. Question is will this make the fan work or is that another issue? Dealer only listed heater core as the problem.