that is entirely possible.
as was pointed out in another thread, it might also be the power supply, if it is external, for the case which is causing the problem.
External cases for external hard drives can be had at Macsales, NewEgg, or places like that.
I purchased a number of them from Macsales and they are still working. Be sure to get one that has its own, external, power supply. Do not go for one of those that uses the USB bus to get its power.
There are some that do Firewire400/800/USB2.0 and eSata but to use to just recover the data on that drive, a USB one will do nicely.