Usually teams have a stage race squad and a classics squad, but in the past tere have been some huge performances from tour riders in races like, as mentioned, LBL which suits a very hard rider. Flanders is not beyond reach either. Just ask big Eddy.
All that said, if some stage race riders are in starting line ups at classics, it's often as preparation (of the right kind) for later in the season, and essentially they work themselves to a standstill for the specialists. Right about little Cadel, he has, or had, a great explosive ability for climbs like the Muur, class always shows out at some point.