I sense much confusion here. Supercritical wings/airfoils, sweep, and winglets are all independent of one another.
A "supercritical wing" refers to one that's cross section is a supercritical airfoil (or a series of them). They're not exactly new (mid to late 70s) and anything with a cruise speed over .8 mach is likely to have one. It could have winglets, it could not. It could be swept or straight (although there isn't much point to a straight supercritical wing).
In turn, a supercritical airfoil is one where the pressure distribution is shifted aft in order to delay the onset of supersonic flow over the wing, hence raising the critical mach number and reducing wave drag.
Sweep is used to increase the critical mach number through a different mechanism. For a swept wing, think of it as a straight wing in a sideslip. The relative wind in this case can be broken down into a chordwise and a spanwise component. Since the airfoil only accelerates flow (therefore changing pressure) in the chordwise direction, it's effectively flying at a lower airspeed than the freestream.
And finally, winglets are used to reduce wingtip vortices and thus reduce induced drag. They can be used on any type of wing.
OK, now that that's all out of the way, back to the original question. And the answer is: I don't know. There are many, many variables when it comes to an airplane's stall characteristics, so I couldn't definitively say one way or another. More than likely, it's a non-issue as the types of aircraft likely to have a supercritical wing aren't going to be stalled very often outside of a flight test environment.
Well, hopefully that's confused the hell out of y'all, so I'll bow out now.
Edit: Sorry, Matt. I guess you weren't as confused as I thought when I started writing this. You're above reply was spot on. Hopefully, this novel has helped someone, though.