Does An Empty Aluminum Can Weigh More If It's Crushed?

No, it still weighs the same, but you sure can get more cans in the recycling bin!
So I believe it is a bonus to go ahead and crush them. That means less trips to the recycling center and less money spent on gas to get you there and back.
It's a win, win situation.

No, lets say you have a piece of paper, you fold it up and its still paper with the same weight. Its only a physical change not a chemicle change. Same thing goes for cans.

Using a very nice high dollar scale at a company I worked for, and several soda cans of different "flavors", I found that aluminum cans actually weighed more when they are NOT crushed. The only thing I'm wondering is if maybe the slightest bit of air that is trapped inside added weight??? Also, maybe some of the cans could have still had a drip or two of soda in them?? Let's just say this was not an experiment that involved billions of dollars of government bailout money!

No way... Unless you add something to the can it is physically impossible for its weight to change just by crushing it.