Windows 2000 Professional as long as other Windows 2000 and XP family operating systems have full support for FAT32 and FAT16 file systems, as long as CDFS, HPFS, etc.
Operating system communicates with file system via logical level Win32 API that, in turn, redirects function calls to physical level (file system drivers), so if proper file system driver is installed, operating system can access and work with file system properly.
Drivers for NTFS, NTFS5, FAT12, FAT16, FAT32, CDFS are always installed when you install Windows 2000 / XP. Drivers for NTFS, FAT12, FAT16, CDFS are always installed when you install Windows NT, there is no built-in driver for FAT32 in Windows NT.