Good Idea. Have done this in the past, but have found the external drives are not of the same quality, usually Hitachi or Samsung, and do not come with the same warranty from the manufacturer. Western Digital and Seagate, for two, will generally not warranty the drive at all unless you also return the case.
But these are desperate times for a while. Western Digital started up production last Thursday, but are still at only 40 percent of their previous capacity.
Soon they will be a full production, but there are big questions about when any of the drive manufacturers will be producing IDE and EIDE drives once more.
Our repair shop prices for 2.5 inch and 3.5 inch drives doubled in price, and in some sizes cost three times as much. The prices have dropped a little from November, but not nearly enough.