One of the first questions that I ask myself about any type of installation is "has anybody else done it like this"? If the answer is NO, I usually assume that there's some reason why it isn't done.
Other than the obvious reasons for not powering your furnace the way that you describe (it gets unplugged, more stuff gets plugged in, you're running 15 Amps through a teeny little wire), there is a Code item that says that you can't do it.
422.16 Flexible Cords.
(A) General. Flexible cord shall be permitted (1) for the connection of appliances to facilitate their frequent interchange or to prevent the transmission of noise or vibration or (2) to facilitate the removal or disconnection of appliances that are fastened in place, where the fastening means and mechanical connections are specifically designed to permit ready removal for maintenance or repair and the appliance is intended or identified for flexible cord connection.
This would apply to a window air conditioner, washing machine, or other item that would need to be disconnected for frequent services or changeout.
Since the furnace that gets built into the house if usually the same one that's there for 20 years, you'll need to hard-wire this one. Even if you try to say that the flexible cord should be there for vibration, you'd need to hard-wire that cord into the circuit.
If you're really concerned about surges, there are several manufacturers of surge protectors that can be wired directly into the wiring. Ask at the local DIY store and tell them that you don't want one that's a plugstrip...they should be able to accomodate you.
If not, I'm sure that one of us here on the forum could give you a steer to a suitable product.
Remember to read the instructions, work safe, and turn off the power when working.