Yes! I believe you can read files on a NTFS partition with a Mac running OSX. But writing to a NTFS file system may be a bit more problematic. I hear it can be done but it's not exactly easy/simple. (It's even harder, if not impossible, for Windows to read/write to the HFS file system which is what OSX uses. Maybe there's a utility/patch/driver to do this but I've not heard of it.)
That's why I usually recommend preparing any shared drive (partition) to use the FAT32 file system since FAT32 is pretty universal - especially when it's plugged into a USB port (hint, hint). Only problem is, FAT32 is limited to 4Gb file sizes on a 2.1Tb partition which could be a problem if you deal with large files such as video.
(Hint: If you only need occasional access to your shared files then you might want a way to keep your hard drive off when it's not being accessed and thus save any wear and tear on the drive. That's why I suggest connecting it to a USB port using something like a USB-to-SATA/PATA adapter.)
But in your case, it may be better if you could use that 1Tb drive in a dedicated file server on your own LAN. But obviously, that would require a second computer or another LAN device like a Drobo. I can't say if that's an option but the ability to access files with other systems from Android to PS3/XBox or whatever might be incentive.