In theory it should but it wouldn't be as nice. BTW icing sugar makes the best shortbread since it isn't gritty and if fake sugar doesn't disolve well you'll have the same issue.
ETA my MIL gave me her awesome shortbread recipe and she eats it and she's diabetic. A few pieces of the real stuff surely wouldn't hurt and would be better than using fake sugar.
Edited by Bluenomi, 28 November 2012 - 02:10 PM.