Let's say that I have a Shroomish in Emerald. It only has Effect Spore as it's ability. Is there a chance when I transfer my Shroomish to Platinum and evolve it, Breloom would get Poison Heal instead of Effect Spore?
Yes, when transferring Pokemon from Gen 3 to 4 there is a chance the Pokemon will change Ability, if the Pokemon had only one in Gen 3.
When Abilities were introduced in Generation III, some Pokémon only had one possible Ability. A number of these species were given a second Ability in Generation IV; if a Pokémon of a species which gained a new Ability in Generation IV is evolved in Generation IV or V, its Ability will be recalculated.
Source: http://bulbapedia.bulbagarden.net/wiki/Ability#Mechanics
I honestly think: NO!
The reason I'm saying this because Pokemon never change their abilities when they level up or evolve. This only works if the evolving Pokemon can learn this ability too. For example, if shroomish learned "Effect Spore", then he will learn "Effect Spore" if transferred or evolved.
Source
Hope I helped! :)