Yes, touchscreens are supported by ClickShare devices: CSE-200(+), CSE-800, CX-30, CX-50 and C-10, see Things to know about the Touchback feature.
Using your touch display to control your computer is supported - (UMT or called Touchback)
Blackboarding and annotation is supported by CSE-200(+), CSE-800, CX-30, CX-50 and C-10,
See How to use annotation and blackboarding with the CSE-800 & CSE-200+ for annotation and blackboarding with CSE-800 & CSE-200+ .
More details about the supported touch displays can be found in the ClickShare Supported Touch Panels whitepaper for CSE devices. This whitepaper can be found on the product page Technical Support > Manuals' Drawings & Documentation. A direct link to this whitepaper can be found at the bottom of this article.
More details about the list of supported touch displays with CX-30, CX-50 and C-10 devices visit supported peripherals overview page .