Say I have an iPhone Camera Roll with 1,000 photos or videos in it, and on my Mac, a folder called "Pictures From Brazil". I want to copy that folder's pictures onto my iPhone, but I want to keep everything in the Camera Roll.
Can I use iTunes to do this (syncing photos using the Photos tab in the iPhone section of iTunes), or if I turn on "Sync Photos" to copy that folder to my iPhone, will that overwrite my Camera Roll and / or remove its contents?
Yes, you can safely sync a specific folder from your Mac to your iPhone via iTunes without overwriting your iPhone's Camera Roll.
You don't specify your version of iOS, but typically what will happen is that the sync will create an additional album in the Photos app on your iPhone. So, using your example, if you use iTunes on your Mac to sync selected albums and then select the "Pictures From Brazil" folder, this will add an album on your iPhone called "Pictures From Brazil".
This additional album doesn't impact your Camera Roll at all.