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I cannot say whether it would damge your engine but why not just take it in and get if fixed since you have a GS for a reason and that is 35 or 40 horses more over the LS model......which is not supercharged.....I can't see where it would be more than $100 if you need a new belt only...?
The car will run with it off, but it will not be good on the engine as the blower also is the intake for air to the engine. You could drive it to get the belt, but I would not drive it much farther, it will damage it. It would also ruin the supercharger in time as well.