What are the conditions and effects of grabbing a suppressed enemy?

Solution 1:

Suppression does not prevent move-block abilities from having their normal effect.

Malzahar's ultimate has a leash range, it is possible to cancel a friendly Malzahar's ultimate by pulling the target out of leash range. If your move block does not place the victim outside of leash range, Malzahar's ultimate will complete as normal.

Warwick's ultimate does not have a leash range (but see below). If you move his victim, he will continue to channel and deal damage while appearing to savage thin air.

This youtube shows a Blitz grab connecting shortly after Skarner's ultimate begins:

Skarner's ultimate will not be broken by move-block abilities - instead, it will override the move black shortly after it begins with its own effect.

ETA: Xypherous recently announced planned changes to Malzahar & Warwick's ultimates:

We're doing a change (or a bugfix, depending on your point of view) on both Warwick and Malzahar. Their ultimates will be treated like leashes... because they kind of are. (You can't QSS leashes. You can only break them via distance.)

What this means is that QSS will break the stunning effect on you but until you get out of range of them, it won't cancel the damage and other effects these characters will be doing. Malzahar will get his full Nether Grasp until they break the leash and Warwick typically gets 2 (maybe 3) more swipes before the target walks away.