I don't have enough information to say yes or no. The smock was introduced in 1942, but it seems like it went through some camouflage and cut patterns before the design we're familiar from in '44. Pockets, openings, there's lots. The paras did seem to suffer from the extreme weather in Africa in their late '42 operations, but I can't find any confirmation or negation of wearing the smocks in the Osprey Elite book, and my secondary source is Commando comics. Given that they use a bazooka (they only seem to use bazookas in Commando comics, never a PIAT, grumble, grumble...), it's probably not all that accurate.