Probably, but it depends on what you’re trying to run.
For a windows desktop, see Remote Desktop Access
SSH and VNC clients exist, and you should be able to connect as from any other computer, but see the Remote Access FAQ’s for details.
Once on the VPN, you can connect to the Windows Terminal Server, animal.eng.utah.edu with an RDP/RDC client.
Or use an HTML5 connection to animal.eng.utah.edu. Just a web browser is required. HTML5 Desktop use the “Login as Guest” button then click the link to animal.eng.utah.edu. You will be presented with a login screen where you should input your CADE username and password.