Short answer: yes.
Longer answer: It depends.
Serious answer: It's application-dependent. The CRX can be put into "unsafe" mode for greater speed or power, and at that point you need some safety-rated means of ensuring no one is at risk while the robot is in that mode. Alternatively, you could lock the robot permanently into "collab" mode, so that it never moves quickly enough to do harm, and is power-limited for how much force it can apply.
For example: I did a CRX job that used a powered screwdriver to fasten a bolt to a specific torque level. The torque, however, was more than the robot could handle in "collab" mode -- it would generate a DCS collision fault. As such, we programmed the DCS to allow "unsafe" mode when the robot was at the bolt-driving position, with only a tiny positional window. This basically gave the robot a higher-torque "unsafe" mode, but only when it was stationary at the position it was needed.
Another issue we ran into was that putting something "sharp" (like the flat tip of an M3 bolt) can make a "collaborative" robot into a non-collaborative one. This is because RIA 15.06 has specific force/area limits for different parts of the human body, and it turned out that the lowest amount of collision force the CRX could reliably detect (without generating "collison" faults in mid-air) was too high, over the area of the tip of the small bolt, to pass the standard limit for the human hand. So we had to protect a few "pinch points" where the robot was moving the bolt directly into a hole before fastening, and someone could potentially get their finger in the way.
So, just buying a "Collaborative" robot doesn't mean you escape regular safety requirements. You have to evaluate all the potential risks, just as you would for a non-Collab robot. It's just that some of the safety is now internal to the robot. Like in our screw-driving application -- if the bolt had been of a larger diameter, the worst-case pinch point would have been protected enough -- no one could have gotten more than a minor bruise before the CRX detected the collision and stopped on its own (I tested this using myself as a crash-test dummy).
OTOH, if your cobot is carrying a plasma cutter or a high-power laser emitter, well, "collaborative" mode isn't going to do a thing to make the end effector safer.
