Although I agree with you that support could be better I don't think this issue is ThinApp's fault. We work in a VDI environment (golden image etc.) and we didn't ThinApp Chrome. We just placed the Chrome files in the image and use Appsense to manage the user environment (some profile files and admx to set policies). We also encountered the issue with the blank icon in the taskbar so it looks that at some point Chrome decided that the icon file that is displayed in the taskbar is not the icon of the main executable but should be an icon in the user profile.
Solution for us was to place the icon in: %USERPROFILE%\AppData\Local\Google\Chrome\User Data\Default\Google Profile.ico