So don't tell them when you drop them. Do the usual CYA stuff and tell your boss and explain to him exactly why you want to be sneaky!

Remember Schrödinger's cat and the Observer-expectancy effect! If they don't know they are being observed then they'll behave as normal. They'll still be complaining, but no more than normal.

Either that or drop the indexes, and the say that you have re-added them after the complaints come but leave them disabled.

There's more than one way to fool a user!