Just to complicate it a bit further, most slips done in anger are to lose height very quickly without any increase in air speed, as in a real forced landing into a small field. So they'll be done with full flap, and in some types, the Cessna 150 family for one, the rate of descent with the engine out, full flap and maximum controllable slip is dramatic.
As some one has said, pitot errors prevent any correct indication of air speed; all I know is that if you keep the airspeed indicating the stall speed for the weight and configuration plus about 10%, using the elevator to control it, you won't stall. Or at least I don't.
But I'm pretty sure that the stall speed must increase, for all the reasons cited above and the diagonal airflow; but that is compensated by the pitot under-reading in a slip.