You've got to decide what your priority is prior to going to the airport.

The bottom line is a guitar is not of size and shape to carry on board the flight. Has it been done? Yes, if the agent is too whimpy to do their job. It needs to fit into a size wise. The company continually reminds their agents that they are not accepted.

If you think it is worth the risk of getting to the gate and being told sorry but no way and have it sent below then the risk is yours. As far as them being damaged, happens often and claims are usually denied since they are checked at the passengers risk.

Buy a seat or buy a hard case that can survive being checked.

You could also apply for Skymiles credit for the seat after you travel. It doesn't automaticaly apply.