If you get the entire folder copied, then you will be OK.
At the time the File Geodatabase was designed, it was well understood the problems from the past copying coverages but forgetting the INFO folder, or copying a shapefile .SHP but forgetting the .SHX and/or .DBF. Efforts were made to avoid those problems as much as possible.
One thing to be aware of is if your File Geodatabase has an unmanaged raster catalog. If you copy the .GDB folder, that will miss the unmanaged rasters since by definition the rasters exist elsewhere in the file system. You will have to take that into account. If your raster catalog is of the managed variety, you don't have to worry, because the rasters are stored in the .GDB folder as tables within the database.
The only other thing you need to be careful about is whether other people are updating the File Geodatabase at the same time that you are copying it. Pay attention to any error messages that occur during the process of copying or zipping.