As I pointed out recently in another thread, the hand thrown type of smoke grenade is of extremely limited value as a screening system. It produces only a brief cloud of smoke and is extremely vulnerable to weather and in particular wind. For the most part such grenades are primarily used as target markers or signaling devices rather than for screening.
When screeing was required it was normal for just about every nation to use smoke pots, smoke generators, or massed artillery fire (hence the German adoption of the Nebelwerfer for this purpose as one example).
I would say in terms of wargaming that a typical infantry unit might have one or two such grenades for marking targets and such, if any at all. As a screen, a couple of hand thrown smoke grenades are next to worthless. On a regular basis I would expect that forward observers and unit commanders might carry around a few but, other than that, I would rarely expect any infantry type unit to be lugging smoke with them.