The ConnectWise PSA (Professional Services Automation) fat client does not work at all due to its dependency on .NET 3.5.
The IE 7 interface can be made to work using a standard install of IE 6 SP1 (6.0.2800.1106) installed in a Win98 bottle. Significant portions of the application (My Schedule, Projects, Reports, etc.) are completely unavailable in this mode. Other portions are generally usable with some UI quirks. Viewing tickets and logging time does work properly, making it usable for me. This beats virtualization, but just barely.
Note that what ConnectWise calls a web interface supports only IE 7.0 (as shown on ConnectWise web site). Normal web browsers (Firefox, Chrome, etc.) will not even get a login prompt.
All information current as of Oct 2008.