I suppose the more relevant question for this election cycle would be that if there IS indeed a significant effect on the voter, what would be the result? I don't imagine that people would say "I'm not voting for a minority -- I'm voting for Obama instead!"
Given the analysis from many pundits that Republicans were casting votes for Herman Cain partially as an over-reactive response to cover for their own suppressed racist sentiments, coupled with the fact that the sitting president is a minority, I don't really see what Romney(?) would stand to lose by having Rice on his ticket (from a race relations standpoint, anyhow).
It was all the rage in 2008 to be able to say "Hey, I voted for Obama; therefore, I'm open-minded!" I don't see that mentality changing in 2012.