Other than the gas running out I don't think it will hurt them to store on there heads, probably not reccomended and it a little odd but it shouldn't hurt them.
I agree that I wouldn't bring a motor home from the lake and store it that way but those don't look like the have seen water for awhile. Water from the exhaust entering the crankcase would be the issue. If you had a leaking gearcase it will just run all over the outside of the powerhead. Wouldn't do any harm but would make a big mess.
That's the preferred method when using E-10 gasoline. That way the carb drains and you don't have to worry about fuel separation or clogging of the jets.
