Any way to get a test install version of Visio 2013 professional that will install on a server with Terminal Services?

The only way to install it on a Terminal Server is with a Volume License.

Is there any way to get that version as a test?

The downloadable version won't install it at all.

Hi,

As Mr. The_Techguy said, Visio 2013 professional when installed on a Terminal server had always required the volume license. I recommend you connect the Volume Licensing Service Center or Microsoft local provider to confirm if there is a trial version for Volume License.

https://www.microsoft.com/licensing/servicecenter/Help/Contact.aspx

Hope it's helpful.

Regards,

George Zhao
TechNet Community Support