Only to a very small degree. An LOP mixture is a relatively weak burn.
Though I am not certain, It's not so much heat or not at the exposed ('cause open) exhaust valve stem which concerns me, it's the only partly burned products of combustion getting and sticking there which worries. me. I do agree that if LOP, probably everything got burned, but it's still flowing past there in a way that the engine manufacturer might not have accounted for in the design.
As for the waste gallon per hour... One of the rewards of enduring a quarter century of ridicule for owning a 150 spam can, is that the difference between wasteful and efficient really is only about a gallon per hour. Now, when I fly the Navajo, things are different!