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I've done something like that before (ginger simple syrup with seltzer and a mint leaf or two) and have come up with a somewhat lighter version of ginger beer (I suppose one might call it ginger flavoured Italian soda), so I don't see why it wouldn't work the same way for you with the ginger beer syrup.
If you happen to have both on hand, why not give it a try? Couldn't hurt and can't imagine that it would taste bad even if it doesn't turn out exactly how you imagined.
