RGB - nope
Composite - probably not
RF out - probably a little
The FCC likes to see shields on this stuff so as to not cause interference across other peoples gear nearby. In practice though, I think it's all a bunch of rubbish that's not so neatly wrapped up and mired in politics.
I remember many years ago the shielding made a large difference in terms of reception of short wave on a nearby radio. With shield = some interference, without shield = totally destroyed reception.
I also remember in my teenage years I had an Atari ST (boo hiss!) that I could 'pause' using my CB radio. Key up the radio and the whole machine would halt - only to continue perfectly when I let go of the mic. I always thought this was a pretty neat trick; but in hindsight I guess this is entirely possible if the clock gets neatly halted.
Shields are there for a reason though, even if you personally don't suffer with EMC issues. In a mdoern house with wifi, bluetooth, mobile phones etc - perhaps there's more reason than ever to have shielding. I wonder how many random miggy crashes are due to a mobile phone sitting nearby and lack of shielding? Just curious

Steve
(operating with A1200 shield removed to create space for internal fans)