Yes, it will work like a champ.
It is my opinion that a gen head with some headroom for surge is a good idea. It is always OK to put too large a gen head on an engine (within reason). The opposite is rarely ever true (for our purposes)(AC power generation). About the only application where a too small system works well is an automotive alternator. But, remember that the alternator never has too much load as designed.
A strong running 12/2 may surprise you with the level of power you will be able to get. Rocketboy can make 11,000 watts with his 16/2, which is more than many would have guessed.
Chris