No-blower running?
 

If I disconnected the supercharger belt and ran my car for a long time and drove it around like that would it mess anything up? If not would I exhibit better fuel economy?

You'll probably foul your spark plugs in a week, but nothing worse. You'll also have worse fuel economy. I gaurantee it.

If you are looking for better fuel economy, change your filter to a K&N panel filter. And make sure your O2 sensor is up to snuff. Around the town economy won't go up much, but highway mileage will.

I had my S/C belt break on me in NC and had to drive to GA, about (350-400 mi). It was gutless, no passing power and the heat from the engine actually boiled the S/C oil and spit it out the breather hole where the S/C pulley is.

Don't Do It