I wouldn't. I'm not really sure what is meant by 'classy', but there are plenty of horses that have come out of the SunAlliance in recent years to show themselves high-class staying chasers. Lord Noelie, Native Upmanship, Alexander Banquet, Jair du Cochet, Our Vic, Star de Mohaison, The Listener, Denman, Mossbank, Albertas Run just some of them. And certainly not all of those are the strong-galloping types.
The types that get 'hurt' in the race imo, are those who have beaten very little by pottering around in their trials for the race and get found out when the are forced to jump demanding fences at a proper gallop and then get shown up subsequently as not being up to it in open company the following season for the very same reasons.