Yes off course you can do that. That is one of the benefits of using virtualization software.

Cloning:
1- Install VirtualBox sofware on target machine.
2- If your virtual machine is runnning then shut it down.
3- Copy the source disk image to the VirtualBox VDI directory on the target host machine. The source disk image resides in the VirtualBox VDI directory.
On Windows hosts the standard path is C:\Documents and Settings\<username>\.VirtualBox\VDI).
4- Now you can register it with VirtualBox on the target host machine.
From the VirtualBox window select File→Virtual Disk Manager (Ctrl+D) menu command.
Press the Add button and select the copied disk image file.

Linux Network:
After cloning you need to reconfigure the linux networking setup. Simply change the IP address to something that is available. For example if your original VM is 192.168.2.14 then make the clone as 192.168.2.15. You only need to do this step if you will be running both machines at the same time.

Windows Setup:
Here you will have an issue if you are using one windows host to connect to both at the same time. If only one virtual machine will be up at one time then you are good. You dont need to do any changes. If not then every thing you connect you will have to make changes to the host file.

If you are connect to the target you will change the IP as:

192.168.2.15 linux.server

If you are connect to the source you will change the IP as:

192.168.2.14 linux.server

One way to by pass this issue is to change the host name for the target to something else e.g. linux2.
Then you can place the following lines on Window hosts file:

192.168.2.14 linux.server
192.168.2.15 linux2.server

You can now connect to both machines without changing the setup again and again.

How to Change Linux Host Name:

As root, open file /etc/sysconfig/network
Change entry HOSTNAME to linux2.server
Change entry in /etc/hosts to linux2.server
Reboot Linux