Mike,
I doubt that you would have to remove ZA to use Norton/Symantec's AV program. You should disable it during the install process of Norton's AV, which may have been the intended advice you received.
Your next statement "Is it a good thing?" is unclear to me.
Should you have remained with Norton 2004; not from my point of view. Norton has become seriously bloated and is not the product it once was with the exception of their corp version. I would suggest searching for a better product and personally use Nod32 as my AV...small footprint and very good detection.