Well, kinda sorta. Remember, back in the day, anything with poison was also SoD. So, giant spiders, snakes, and a whole slew of other fairly common critters could bypass HP. And, if we have to signpost monsters, that's a pretty poor monster design. I mean, sure, one adventure with statues in it, signposting that medusa is interesting. But, it gets pretty silly to think that every medusa (hardly a stupid monster) would be so careless as to leave evidence around. Never minding creatures like Bodak's which have SoD, but, then eat what they kill. Besides, even if you leave statuary around, what does that really tell the PC's? That it's a medusa or a cockatrice or a basilisk? Or a Medatrisk?
And, even if we do signpost it, so what? The party is going to turn around and run away when they see statuary? Not likely. They're going to push on, still meet that medusa, and still be forced to make that saving throw. It's not like you can really avoid it.
I really dislike the idea that certain creatures have to be signposted, thus very limited in how they are used, just to smooth over what are, IMO, bad mechanics.
Invisible Imp in 2e had a SoD poison stinger. I have a wonderful low level Dungeon Magazine adventure that often claims the life of a PC called the Wizard's Fate. There is no way in heck he's going to announce himself at the first encounter, of course his ring of spell storing helps him in this regard too... Sting the PCs in the back of the neck while they fight the demonic illusion is more his style anyway.
