As one of only 4 states to vote Democratic at least twice in the 1980s (MN, HI, and RI being the others) I'd say yes. Remember though that the complete switch takes decades, in fact, a lot of southern states (particularly Lousiana) still haven't changed that much at the local level. Despite the poll mentioned in another thread, Byrd has at least one more re-election and Rockefeller doesn't seem to be in too much trouble either. That's the problem with sudden changes in voting patterns, there's no big candidates for the emerging majority party.
at least until the big-name figures in question decide to switch parties the way Strom Thurmond, Phil Gram, and Richard Shelby (among the most prominent names i can remember off the top of my head) have done.
that said, i am not overly familiar with West Virginia politics, so i do not know any major political figures who seem the most likely to switch from the Democratic Party to the Republican Party.