If some action is a waste of resources, then who provides the resources doesn't change whether it's a waste or not.
In this case, if sending a signal into space takes a lot of energy and if energy is scarce, then it's a waste of energy regardless of if the government provides it or a private donor.
EDIT: I'm not saying this is true in this particular case (I'm also not saying that its not true), I'm merely stating that whether something is a waste doesn't matter on who is doing the wasting. I would gladly listen to a counter argument and maybe a discussion can be had, but I guess its easier to click a down arrow. Oh well. (Yes, yes, I know it'll happen even more due to my mentioning it)