Unfortunately, being able to copy an application like this is going to depend very much on the application itself. Some you can copy, more you can't because of the fact that they are quite often installed all over the place... e.g. the pap folder, the Windows folder, the Windows System32 folder... and other places. Sometimes, issues with copying like this can be resolved by installing libraries and stuff... not easy to give a categorical answer though. Try it and see what happens.
If the server is not recognising the USB HD, you may need to copy the files to a workstation PC across the network and from there to the USB HD. Windows 2000 should recognise USB devices though.