Do mods or console use disable achievements for Fallout:New Vegas?

The best source I have for this is the Fallout Wikia. They say:

Please note that cheating, on the PC version at least, appears to disable achievements for that play. If you are cheating (or using console commands to get around bugs) , you won't get any achievements unless you save, quit, reload, and redo the achievement.

Unfortunately I can't test this myself, but this seems to stem from experimentation.

Oh, seeing as you mentioned it: I'm fairly sure using cheats will not remove any achievements you've earned before. That's just the way Steam works.

Update: Using mods does not affect achievements at all. Only console commands are construed as cheating.