Riot games have put a special effort into having balanced champions for this game style as well. I don't believe there are any champions to avoid. However, the team composition changes a bit.
AP Carry
You will still need one, or else the other team will just build against AD and will own you as soon as they are a bit stuffed.
Tank / Off Tank
King in solo holding the bot lane, also very good in "tower diving" (if we can still call it so in Dominion).
Melee Fighters
They tend to be the heroes everyone picks as they are sort of kings on this map. They deal quite some damage and have high sustainability (so they don't need to Back often), and are often very good in 1v1 (which happens pretty often in Dominion).
Ranged AD Carry
More than one is too much, but not having one (to have more fighters) is a handicap. He deals crazy damage and can attack out of tower range or defend minion waves without exposing himself in front of the tower. From the games I've played or seen, having only melee champs is clearly a handicap.
Support
I rarely see them in Dominion and believe they are overlooked. Each time I've had one on my team, it was awesome to hold the windmill (we never had to back, support would always buff/heal us).
However, having a support requires good team play, because the champion won't do anything on its own (compared to fighters).
General
As XP gain is so fast in Dominion, teams are usually built with mid/late game champions. Riot tried to correct this in a previous patch by lowering the XP gain aura on the map, however, you still get to level 6 tremendously fast, so don't hesitate in taking weak early game champs (like Kassadin, useless before level 6).
Try having a hero or 2 (at least) with high mobility (Rammus, Kassadin, Nocturne, Twisted Fate, etc.) to do lane swaps and be unpredictable in your tower attacks.
Conclusion
All heroes are viable. It all depends on the team composition.
Good Akali, Irelia and Xin Zhao champions can however be freaking awesome with their ganking abilities and life steal.
It's generally only beneficial if you are a) the jungler and have smite up and b) have current vision of the Baron so you can see the life
If both of those are true and you can properly watch how fast the health is dropping, then it is possible to jump in and actually steal it. If you can flash over, noc ult, or the BEST WAY to steal Warwick ult the Jungler when it is low and steal it then it's worth it as a way to "bring back" your team from losing.
The reason WW ult is the best way to steal is simple; WW ulting "surpresses" his target, meaning they can NOT cast ANY spells including Summoner spells. So by ulting their Jungler when the Baron is low you ENSURE he cannot smite it, and most of the time your ~800 damage smite can ensure a steal.
As a side note - if dragon is up and A and B are not true, it may be the best bet to go and steal the dragon/take a tower before backing and defending your base.
Best Answer
No, Only Kalista and the champion you made your oathsworn can see te link