I read your other topic on dialogue. I'm a bit confused what you are trying to do that means it is not a quest that you are after?
Quests don't have to be things-that-the-player-must-do - Beth often uses quests as somewhere to put scripts and control mechanisms, because you can then easily use things like Quest Objectives which appear in fancy text in the middle of your screen.
For example, the Khajiit Caravans are controlled by a Quest, but that Quest is nothing to do with the player and has no Objectives and so on. Beth just used the Quest as somewhere to hang all the relevant scripts from. So, you could use a Quest for your Dialogue and to write things to the middle of your screen, without the player having to have any effect on the "quest" at all. I guess it depends on what you are trying to achieve?
As to this question, I haven't seen anyone report a way to do what you want, debug.notification always appears top-left of screen. However, at the back of my mind something tells me someone did report a way to do this, without quests, but searching here I can't find it (so I may well be imagining it!)