yes, that's how most industria lCO2 lasers work. The laser itself is somewhere safe, mecahnically stable and with lots of cooling. A fibre carries the laser power to the cutting head. Often they even have a separate small visible laser fibre wrapped around the main bundle - if there is any fault in the power bundle and the beam leaks out it quickly burns through the optical fibre which is detected and the laser shuts down.
Fibres are also used to bring the power from several lasers heads to one point, although this is more common with diode lasers.