ThinApp runtime in it self should not care if there is a C-drive available or not. The application packaged might. You can virtualize drive C so it is available to the application. If GPO settings hides the C-drive for the application can you disable GPOs in the package.
More info:
http://blogs.vmware.com/thinapp/2010/10/thinapp-and-group-policy.html
http://blogs.vmware.com/thinapp/2009/12/the-packageini-file-explained.html
Peter is correct on all accounts.
However, on the off chance running a ThinApp packaged app which was captured on a clean Capture and Build VM which has a C: drive ends up failing when running on a Windows OS which doesn't have a C: drive (as in your case), then you can always remap the root drive of the Clean Capture and Build VM prior to doing your ThinApp Prescan/App Install/Postscan/Build.
I believe Citrix's DRIVEREMAP.EXE tool still resides on the XenApp/MetaFrame/Presentation Server install cd. Just copy that to your clean Capture and Build VM and run it on there as it shouldn't be Terminal Server OS specific.
Hope this helps.
-Dean F
http://pubs.vmware.com/thinapp4/help/
