Yes, it can be achieved. VirtualBox offers this functionality:

VirtualBox can display virtual machines remotely, meaning that a virtual machine can execute on one computer even though the machine will be displayed on a second computer, and the machine will be controlled from there as well, as if the virtual machine was running on that second computer.

(Chapter 7 of the official documentation)

From the same chapter:

Oracle provides support for the VirtualBox Remote Display Protocol (VRDP) in such a VirtualBox extension package. When this package is installed, VirtualBox versions 4.0 and later support VRDP the same way as binary (non-open-source) versions of VirtualBox before 4.0 did.

VRDP is a backwards-compatible extension to Microsoft's Remote Desktop Protocol (RDP). As a result, you can use any standard RDP client to control the remote VM.

Finally, the documentation offers examples of how to connect to remote VMs on Windows and Linux:

On Windows, you can use the Microsoft Terminal Services Connector (mstsc.exe) that ships with Windows. You can start it by bringing up the "Run" dialog (press the Windows key and "R") and typing "mstsc". You can also find it under "Start" -> "All Programs" -> "Accessories" -> "Remote Desktop Connection". If you use the "Run" dialog, you can type in options directly:

mstsc 1.2.3.4:3389

Replace 1.2.3.4 with the host IP address, and 3389 with a different port if necessary.

And on Linux;

you can use the standard open-source rdesktop program. This ships with most Linux distributions, but VirtualBox also comes with a modified variant of rdesktop for remote USB support (see Section 7.1.4, “Remote USB” below).

With rdesktop, use a command line such as the following:

rdesktop -a 16 -N 1.2.3.4:3389

Yes, it can be achieved. VirtualBox offers this functionality:

VirtualBox can display virtual machines remotely, meaning that a virtual machine can execute on one computer even though the machine will be displayed on a second computer, and the machine will be controlled from there as well, as if the virtual machine was running on that second computer.

(Chapter 7 of the official documentation)

From the same chapter:

Oracle provides support for the VirtualBox Remote Display Protocol (VRDP) in such a VirtualBox extension package. When this package is installed, VirtualBox versions 4.0 and later support VRDP the same way as binary (non-open-source) versions of VirtualBox before 4.0 did.

VRDP is a backwards-compatible extension to Microsoft's Remote Desktop Protocol (RDP). As a result, you can use any standard RDP client to control the remote VM.

Finally, the documentation offers examples of how to connect to remote VMs on Windows and Linux:

On Windows, you can use the Microsoft Terminal Services Connector (mstsc.exe) that ships with Windows. You can start it by bringing up the "Run" dialog (press the Windows key and "R") and typing "mstsc". You can also find it under "Start" -> "All Programs" -> "Accessories" -> "Remote Desktop Connection". If you use the "Run" dialog, you can type in options directly:

mstsc 1.2.3.4:3389

Replace 1.2.3.4 with the host IP address, and 3389 with a different port if necessary.

And on Linux;

you can use the standard open-source rdesktop program. This ships with most Linux distributions, but VirtualBox also comes with a modified variant of rdesktop for remote USB support (see Section 7.1.4, “Remote USB” below).

With rdesktop, use a command line such as the following:

rdesktop -a 16 -N 1.2.3.4:3389