I don't know if SAR personnel scan those frequencies as part of SOP. Kind of agree with others, I'd invest in a PLB if that's what you're using it for since at least it will be a more reliable means of signalling help, whereas an FRS/GMRS/HAM will only raise someone if all the conditions happen to be right.

HAM radio would certainly be better than FRS/GMRS in most cases. You can find them for $30-40 and at popular destinations you'll likely find a repeater. Technically you don't need a license to broadcast if you're in an emergency, but it doesn't really make any sense to carry the weight if that's all you'd be using it for. It's super easy to get licensed, a day of studying and a day to take the test and you're done.

You'll learn a lot too.