While poisoning someone to make them sick isn't all that terribly difficult, actually killing someone with poison is. Lethal doses of poison, at least enough to kill a full grown man, are pretty big by and large. So, yes, the two tier model works pretty well here. Arsenic isn't exactly difficult to manufacture but, delivering enough to someone to actually kill them takes time.
Of course, any noble with the werewithal is certainly going to have poison detection magics scattered about his home. Detect poison is a zero level spell - a permanent item that glows when brought within 5 feet of poison would be a minor cost at best.
I really don't think deliberate poisoning in a DND setting would work all that well. It's too easy to detect and get around. Now, if you want to get grim and gritty and talk about poisoning from wounds, poor water and that sort of thing, that's another story.
Not my kind of game, but, it's possible.