Genetic drift in evoltution can occur in evolution through natural selection as a result of not only a positive trait, but from a neutral one. The a trait mutates that does not give any significant advantage or disadvantage to an organism, it can continue to exist and can spread through the population. This spread will not be as quick as a gene providing and advantage, as it is a less active (or passive) process.
In the case of snoring; Yes, a noise indicating sleep could alert predators (or aggressive organisms of the same species) that an animal is sleeping, implying that it is the safest time to attack. However, the number of instances where this can occur may remain minimal, making the trait relatively neutral over the total population.
I'm no expert when it comes to snoring. It would be interesting to see at what level snoring evolved. I know dogs snore, although I've never seen a cat do it. I would imagine all primates will.