That would be ideal and is a good lesson for those that have setups that can accommodate that. In my case, the regulator is in the basement, so combining both into one GFCI is not possible (all tank apparatus are plugged into a UPS which, in turn, is plugged into an inline GFCI). For me, the lesson is to never power-up the filter, after being off for more than a half-hour or so, without bleeding-off the reactor contents. Many a fish gave up their lives to teach me this.
Ugh sorry to hear about your fish.
Going forward could you plug a power strip into your gfci and run everything including your co2 off of that power strip?