Yes, exactly this. Although, fire codes do create a requirement here. You have to be sure not to create places where fire can propagate. And please use plenu

Yes, exactly this. Although, fire codes do create a requirement here. You have to be sure not to create places where fire can propagate. And please use plenum-rated cables (fire retardant sheath). If you have punched holes in your old chimney in order to pass cables in and out, I'd do a fire propagation audit and mitigate any problems that you find. 40 years ago, the U of Minnesota built a new Elec Engg building. As I remember it, every single office for faculty and grad students, as well as every lab, backed up to a secure 6-foot wide hallway that was built specifically to be a cable chase. Brilliant idea. Experimenting with a new technology was a matter of changing out the access plate in the back wall of the office, and rounding up someone with a key to the hallway.