For me, no. I don't really bother with arena. I never said I am the best ARENA player, but when it comes to BGs (whether it's random, or rated) no one, like NO ONE can out-damage me. It's mathematically impossible. But hey, you already know that. I've been working on my spec for a long time to maximize my damage input in BGs with proper usage of cds.. Again, if it's easy to do damage then why am I always #1 on damage even though I'm usually fighting good players like Kaspi, Bgherg and the so-called 2 man army Arcane and Luminy? That fact that you have a higher arena rating than doesn't essentially mean you could dish out more damage input than I do. I once fought a Gladiator ret paladin who had 2 pocket healers in a BG and i still manged to triple his damage.
If you still think that doing damage is easy, then consider doing this:
1. spec Boomkin
2. Get a flask of the Draconic Mind and a few Volcanic Potions.
3. Join a BG.
4. Once the BG starts get the Berserker buff and start dotting everything that moves till your fingers bleed.
5. Forget about the objectives and just keep dotting everything in your way.
After you've done all of that, you would barely end up doing 3-4 mill damage or "maybe" 5 mill damage if you get lucky enough. But still, I would be doubling or even tripling your damage without much trouble.
Again, I'm not that good as an arena player but when it comes to dealing damage in BGs, I can do that very well.