can you convert a unleaded gas engine to run on compressed natural gas?

It can be done. I had a ford camper once that ran on gas or propane by just flipping a switch. The only thing is propane is getting outrageous so you won't save much, especially with the cost of converting it.

If you happen to have compressed natural gas, it would probably work just fine. You'd have to fool with it to get the mixture correct for the various throttle settings; there are carburetor kits available that'll do this for you. Note that compressed natural gas is not the propane you use for your backyard grill. Compressed natural gas requires an elaborate refrigerated tank because it's made of methane, which doesn't liquify so easily. Propane is far better behaved, and you can run a car on it as well. Note that you probably won't save a dime with either of these gases. They're both expensive, and you'll eventually want to pay your fuel tax before the authorities catch up with you.