A disc's region protection exists in the main .ifo file of the movie. When you backup a DVD Video that is only intended for a single region, most software can/will make the backup image "all region" by modifying the .ifo file. If you then burn this data to a disk, that DVD will not be region restricted. If you tell the DVD backup software not to remove the region restrictions, or not to make the disc all region, then the image will still be restricted to a specific region and when you burn the data, the resulting DVD will be region locked like the original was.
The region of burned discs is not related in any way to the drive itself or its region counter.