I think most UK English speakers would use it or be familiar with it - I'm not aware of it being a regional thing. It means to play or mess about (larking about), and also gets used as a noun in sentences like "I've had enough of this cleaning lark" = this cleaning nonsense (roughly). I found this after asking the question: http://www.etymonline.com/index.php?allowed_in_frame=0=larking
The English word "play" covers both "spelar" and "leker" in Swedish, but there's a difference in meaning between those two words. leker is used for free games without rules. spelar is used for playing musical instruments, games you can win or lose at, all games with rules.
So no, it's not at all natural to say that the cat spelar, quite the opposite.