^I doubt it, since, among other things, I don't think TV producers would pay that much attention to theater, or think that their audience would have any awareness of it.
Also, if you're implying that they were deliberately trying for similarity to Sherlock, I think their tendency would more likely be just the opposite -- to make the show as distinct from Sherlock as possible so that it can stand on its own and not be dismissed as just a copy (and so that it can avoid inquiries from the BBC's lawyers). I mean, they've changed the setting, changed Watson's sex, constructed a different backstory, etc. If anything, they most likely cast Miller despite his connection to Cumberbatch, not because of it.
Also, if you're implying that they were deliberately trying for similarity to Sherlock, I think their tendency would more likely be just the opposite -- to make the show as distinct from Sherlock as possible so that it can stand on its own and not be dismissed as just a copy (and so that it can avoid inquiries from the BBC's lawyers). I mean, they've changed the setting, changed Watson's sex, constructed a different backstory, etc. If anything, they most likely cast Miller despite his connection to Cumberbatch, not because of it.