Short answer
No, unless you want it to. The aim is to let people use approved AI tools safely, and stop sensitive data rather than whole tools.
In detail: Does Cloudflare AI Security Block Staff AI Use?
Policies can allow, isolate, redirect or block each AI app per user and group, and prompt inspection catches sensitive data on the way out. Most organisations start by seeing which AI tools are in use, then steer people towards approved ones.