I followed that link and read the proposed law. It only talks about "shall issue" of a concealed carry permit, the CBI's duties in processing applications for a permit, and a valid CO CCW being a satisfactory replacement for a background check at Gun Shows.
So my understanding is that this law would only make a CCW a valid substitute for a background check at gun shows.
Are gun shows treated differently than storefronts right now?
ETA: this is the only portion of the law that makes mention of an exemption from the background check if one posesses a CCW.
"12-26.1-01. Background checks at gun shows - penalty. [ . . . ]
(1.5) A transferee who holds a valid Colorado handgun permit and presents it to a gun show vendor at the time of transfer or attempted transfer of a firearm is exempt from the background check requirement specified in subsection (1) of this section."
And the Bill Summary says, "[SB 157] Allows a person to satisfy the statutory background check requirements for transfers of firearms by presenting a valid Colorado concealed handgun permit to a gun show vendor."