Well, yes, technically, a mid- or long-cage RD should be used with a compact (not necessarily limited to compact, but any front combination with that large of a difference from largest to smallest chainrings). The reason is because the RD needs to be able to absorb the slack in the small-small combination and also allow the big-big combination to run without being too tight. Worst case depends a little bit on chain length. If you have a short-ish chain and you shift into big-big, you could potentially destroy your RD. If your chain is long-ish and you shift into small-small, you might have some chain slack which could cause shifting problems.
Fortunately, though, Shimano has a lot of buffer in their specs, and many people (myself included) find that running a short-cage RD with a properly-sized chain on a compact (50/34) works just fine, even in the "bad" gear combinations (big-big and small-small). It's just that the margin of error is reduced, and you may have trouble if you switch cassettes or whatever.
I'd say: if you have the time to wait and the place you bought it from has a good return/exchange policy, go for the GS. But if you feel you're "stuck" with the SS, go ahead and use it. Just be careful sizing your chain, stay out of big-big, and you'll be fine.