Final Cut Pro, read/write via External Hard Disk
The short answer is yes.

However, I would definitely suggest using at minimum, a USB 3 drive, but for best performance you will want a Thunderbolt drive.

To give you an idea of what the performance metrics of different interfaces are, I've compiled a quick summary:


SATA III (Internal Hard Drive) - 6Gpbs
USB 3.0 - 5Gbps
USB 2.0 - 480Mbps (or 0.48Gbps)
Thunderbolt - 10Gbps


So, while you can use pretty much any external drive, how well it performs is completely dependent on what architecture you use to connect it.  My recommendation is go with Thunderbolt.