The hard drives inside external enclosures are standard drives. If you can get the case open, you can remove the drive from the case and use it in your machine.
The biggest risk you face is that the drive inside the case may not have the same interface type as your motherboard. For example, if you have a motherboard that only has SATA connectors and it turns out that the drive from your external case is an IDE drive, then you've got a problem.
If your external drive has an eSATA connector, you might just be able to use that to connect to your computer - it will have the same performance as an internal drive.