I don't know a lot about thoroughbred bloodlines, but I'd like to say that crossing the two wouldn't be that bad of a thing as far as the fact that they have the same horses in their pedigrees. It's called linebreeding, and when done responsibly, can produce amazing horses. This is often done with show horses and race horses, and often results in a great foal. However, when done irresponsibly, a lot can go wrong.
Being that we're talking thoroughbreds, yes, the right lines help a horse's chance at being fast, unfortunately, until that offspring is in training at the track, there is absolutely NO guarantee that the foal will be a fast runner that will place or win in a race. Some of the best race horses today, have full and half siblings that have been sold for less than $2000.
So if you're up to it, go for the breeding and see if your foal comes out as a nice prospect. :)