Of course, you will have to modify it, if you want to run it in the same network.
Servers usually have a fixed IP address, so I guess the first conflict would be on this level, and you would have to propagate your changes also to database connectivity (if running in the same database, you'd need to create a different scheme anyway), URL, etc.
I'm not sure if this exercise is even worth trying - installation of a new 10g instance is really easy, migration of components and configuration as well, the only challenge might be migration of content, but unless you have millions of items, the Archiver might do it OOTB...
I'd also ask if there is a disaster recovery in place (in case the server blows up), because creation of a mirror site might be a good exercise to test how effective the DR is.
And where do you store documents - in the database, or in the filesystem? If in the database, you might backup the database in one system and recover it in the other. If in the filesystem, then I'm sorry - just out of curiosity do you backup your system? And if so, how - just dump the VM image to another disk?