I really like this idea, I feel like it would be a good "just-in-case" mechanic if Sleep becomes OP that allows the GU team to print more sleep cards without having to fear that there's no counter to them.
Anyway, I don't think the sleep mechanic needs to be nerfed, but rather just the BWD deck, since it is the only deck that utilizes sleep to get such high WRs. Other than your proposed Vigilance keyword, the team could also simply buff aggro decks so BWD can't win against them 😂 Although I don't think this change would be well received...
Agree, having anti-sleep abilities might be good as well to give the GU team more freedom to put out more sleep cards and make a more exciting meta.