I am attempting to add dialogue to some Vanilla NPC's. However, the dialogue tutorials I have used all claim that you need to create a greeting for the NPC, then use the addtopic command. I would really prefer to simply add the topics to each NPC, without altering their greetings. Is that possible?

Yes.
Just make the actor the target of the conditions you want them to say, and use some other method to add the topic to the player (like a quest script).

Thank you for replying! However, I did try that... I made the dialogue condition (GetIsID NPC: 'Adamus Phillida 1.00), and I used the following quest script to set the dialogue:

scn UDImperialCityscript

short DoOnce

begin gamemode

if DoOnce == 0

addtopic HieronymusLexADAMUSPHILLIDA

set DoOnce to 1
stopquest UDImperialCity
endif
end

I am obviously missing something, because the UDImperialCity Quest does not affect Adamus Phillida at all. If you have any ideas, please let me know!

Yeah, remove the line "stopquest UDImperialCity". If the dialogue is attached to that quest, it won't exist when the quest is stopped. If you're concerned about processing, a quest script which only has one condition and ends right away won't have any significant resource impact. If you're super concerned, you could always just use an activator somewhere that adds the quest to the player within an onload block when the player enters that cell. But, even this won't make much of a difference compared to the quest script since you need the quest to be running in order for the dialogues to work.

Thanks again for replying. Unfortunately, the change to the script did not do anything. Also, suppose I was adding dialogue to alot of NPC's. An enormous amount of dialogue in fact, what do you think my best options would be?

Adding alot of dialogue to existing NPCs is a bad idea since this usually creates conflicts and unclean dialogue. Your best option would be to make new NPCs and use those wherever possible, or use an indirect (nothing pointing to that specific NPC so that the NPC form doesn't get changed) means of associating the topics to the NPCs (such as a faction (can use specific rank/gender to differentiate between actors) added with a quest script that has dummy members who are of every race/gender (to get the lip and silent voice files registered right) you are using).

The problem might also be due to your long topic names. With something like this, it's best to start out small and get it working right before you try expanding it to more actors. Depending on what your dialogue conditions are, one small error could be what is preventing them from working, more responses means more chance of error.

You should of course make sure that your script is running properly, that it compiles, and is attached to the quest.

Thank you very much Vagrant! I changed the topic names. They are much shorter now! Somehow that worked (if anyone could tell me why that is I would be gratefull). I am actually working on something like LGNPC's for Oblivion. It's a lot of work, but I'll keep on it --- slow and steady. I've already got quite a bit of dialogue written out. If anyone else has any suggestions for how to avoid dirty dialogue (I'm given to understand that using the quest window, which I have been using, helps to prevent this?) and get my quest working please let me know!