I would say that anything that can be applied to spell-like abilities could be applied to a warlock's invocations, but I don't even think that I would allow this feat to be applied to a spell-like ability (maybe a different feat, with the same affect but for spells and invocations...).
Well, really you should check with your DM before you do anything, and don't act like your trying to get 1-up on him AT ALL! I dm, and I've shot down a few ideas just because the player seems to be trying to pull a wool over my eyes. I tend to "reconsider" later, after the players have thought about it for a while (try again if your dm says no, but don't badger him).