Is there going to be any difference between copying and pasting the contents of a sequence into another sequence vs. just loading that sequence into the viewer and dropping it into the new sequence, in terms of output quality?
There is no difference in the quality of your export. As far as nesting creating problems, that depends on the length and complexity of your timeline, and what you're going to do with it afterwards.
In my experience, there are times when nesting is very helpful, and speeds up my workflow immensely, particularly when I've worked in on-air promos with projects for regular clients. However, the way editors organize their projects is very subjective.
For the most part, I'm inclined to agree with Shane Ross that it can cause issues. Usually though, I've found that those problems are more of an organizational nature than anything else. My biggest peeve about nests is that if you have to add length to them, you have to copy and paste the entire nest (or its contents) into a new sequence, lengthen them there, and re-paste it back into the main timeline. Not always, it's just easier if you have loads of overlapping cuts and video tracks.