Depends on all sorts of things.
For a start, you could give us a clue as to what operating system you're using, and what the "external memory devices" are, and how they are connected to your system.
If you're using Windows, and the external memory device is a hard disk, and you connect by mapping the hard disk to a drive letter, then you can certainly copy whatever files you likem, but unless you cause the new disk to have to have the same drive letter as the old one used to have, then anything that involves paths stored in the registry (or elsewhere) is likely to stop working. So, some applications will continue to work perfectly, some will continue to work partially, some may not work at all, if you don't get the drive letter right.
Many many other scenarios are possible, until you give more information.