I think it depends on how dirty it is. I also think that some of these 'dirty' top case issues isn't really related to dirt.
I had a 'dirty' top case and no amount of cleaning with Magic Erase would clean it. This was during the time when there was a huge issue with yellowing/browning top cases. I ended up getting a MacStyle to cover the ugliness and waited until cracks eventually showed on the top case, which a Genius recently replaced. The new top case appears to be less prone to staining (at least I haven't noticed anything yet).
Dirt cleans off. Anything that alters the chemistry of or bonds to the top cases won't come off.