You mean crack open the external enclosure and replace your computer's internal one with that one, or just boot from the external drive through firewire or usb?
If the former, probably, if it's a laptop-sized hard drive and SATA. If you want to just boot into OSX from an external hard drive, your computer would run very slowly and I wouldn't recommend doing this. I'd suggest keeping OSX and your apps on the internal drive and store media and personal files on the external drive.