Absolutely! Some of those NASCAR haulers have machine shop tools in them. It would be very dependent on pre-planning and proper securing of the shop tools and benches. You would also need a strong generator with clean power.
As far as working while moving, Dangerous as well as illegal.
On the business plan front, what is the need for a mobile shop? Would the extra expense be something that customers would be willing to pay for? How would you market such a beast, and who would be your target market?
Doc Weaver '98 Freightliner FL60 pseudo toy hauler