I suspect that occasion when Noel Edmonds appeared in the Broom Cupboard after Noel's House Party was abandoned could be the only time Tom and Jerry was introduced in vision from the Broom Cupboard
This is EXTREMELY pedantic but there were screenings of Tom and Jerry on CBBC. The "programme" the Beeb made mentioned up there was Tom and Jerry's Greatest Hits which was, basically, three Tom and Jerry cartoons stuck together with a Beeb-produced title sequence, and if you look at saturdaymornings.co.uk and look at the scripts of both the last Going Live and the first Live and Kicking you'll notice it was shown before both programmes, and in those days Saturday mornings were linked from the Broom Cupboard.
There were some cartoons that weren't generally shown on CBBC, though, The Flintstones was one which would often be shown before or after CBBC, at 3.30 or, before Neighbours, at 5.35, but I'm pretty sure that it was almost never shown during CBBC. I remember someone writing into Andi Peters' column in Fast Forward in 1990 asking why BBC1 stopped showing The Flintstones at 6am before Breakfast News, which they did for a while, I remember watching it, and Peters said it was because Nicholas Witchell was watching it rather than getting ready. He said it was apparently too expensive to show at that time and I also recall he said it was actually bought as an adult show rather than a kids' show, hence why it was currently being shown at 10am. Although later I remember it being shown on Going Live, and maybe another Saturday morning show?