Since your external options on that computer are basically FireWire or USB2, the disadvantage (aside from the obvious of having an external dangling off of it which needs to be plugged in) is that it'll be somewhat slower. Modern hard drives can generally output more data than the amount either of those connection schemes can handle, so while it probably won't be a dramatic slowdown, it isn't the most efficient way to run.
Other than that and the potential to accidentally unplug/power off/whatever the external, at least in theory there's no other real disadvantage. Can't say I've done it for more than emergency purposes, though.
Question: Are you wondering if it'll work so you can get things reorganized while you replace the internal drive, or are you considering running it full-time off the external? If the latter, keep in mind that the internal drive in the MBs is really easy to replace--it's accessible through the battery area.
