The Bradley effect is pretty small in the first place, even smaller amongst Democrats, and even smaller than that amongst Democrats committed enough to go to the caucus. It won't be an issue.
While I agree that the Bradley effect is small in Democrat primaries and caucuses compared to in general elections, I disagree that the Bradley effect is completely negligible among Democratic voters. I believe it may very well be relatively significant, particularly in predominantly caucasian states such as Iowa and New Hampshire, for example. Go read up on the polls that pitted Jesse Jackson against Michael Dukakis in 1988, especially in places like Wisconsin, and compare them to the actual results. There is no doubt the Bradly effect was significant in 1988 in a number of Democratic primaries and caucuses.
As for 2008, this is merely a suspicion on my part. I may be wrong, and I actually hope that I am. We will find out Thursday.
The Bradley Effect may still be a factor. But much less of one than back in the 80's. First of all, Obama isn't involved with Jackson, Sharpton, Lewis, etc. so he is seen as being separate from the black establishment. Second of all, people are less racist today than they were then. I'm not saying racism is dead, but its far less acceptable or widespread than in 1988. And thirdly, if people have last minute doubts about Obama, it will be because of his supposed inexperience, not his race. (Also, getting his supporters to show up at the caucus will make a big difference).