Not unless you really put the plates into a lying down position in torkstället (I call it diskstället btw), but since they would dry very slowly that way, I don't recommend it. The normal way diskställ are contructed, they support the plates so they can stand on their side to dry quickly, so we say ställ tallrikarna i diskstället.
This makes sense, but it is not coherent with the table situation: one uses "ställ" in both cases, but the position of the dishes is very different. I fancy a conversation like "Var ska jag ställa tallrikarna? Det finns ju ingen plats alls på bordet." "För ögonblicket sätt dem på stolen." "De finns ingen plats där heller." "Jaså, lägg dem på sängen då."
It is coherent, because there are 2 different ways for plates to be in a standing position. Either the normal one, standing on their 'tiny feet' on the table, with their upside upwards (so that they fulfill their intrinsic orientation), or standing on edge, which they can't do without support.
Your examples work though, you can use sätt to talk about temporary placing things, for one thing because then you focus on the 'placing' aspect of it, not on how they will stand. And on the bed they would also not quite fulfill their intended intrinsic orientation, so either lägg, ställ or sätt could work for that case. (assuming you're just talking about getting rid of them, not using them)
I had a thought about lägg vs ställa in cases like this.
In English, when I think about whether I would say "lay" or "set", this difference really comes down to what the person is doing, not what they're doing it to. Lay to me means 'to put on the flat side'. I wouldn't tell someone to lay a ball on a table because balls don't have a flat side. I think if someone told me to lay a ball, I would wonder if they wanted me to deflate it first.
On the other hand, set to me means 'put and make sure it's stable'. Even if something were flat and you COULD lay it, you could still set it.
If someone told me they 'laid' a tube down, and I find the tube standing up, I think they're lying.
If someone told me they 'set' a tube on something, I might be surprised to see it standing up, it's not a lie.
If it works similar in Swedish, this might help people better intuit things.
I think English speakers might struggle a bit, because we usually just use 'put' as a catchall.