We really hope so, but even given our so far successful reintroduction of the martens here in mid Wales it will be many years until they are at densities to make a significant difference - if they do. But our martens are breeding and spreading their territory, our few remaining reds are very illusive but just about hanging on.
There's some evidence of buzzards taking reds, think on the isle of Wight they had some concerns as the buzzard population began to increase. If one sees a buzzard with a grey it's hard to know whether it was prey of scavenged road kill?