No I don't think you can install the Desktop program on a Chromebook, not the CD and not the Download. Does it run a full version of Windows? Where does it say you can?
Window System Requirements
https://ttlc.intuit.com/community/system-requirements/help/minimum-system-requirements-for-turbotax-...
Mac System Requirements
https://ttlc.intuit.com/community/system-requirements/help/minimum-system-requirements-for-turbotax-...
