I just took my Gossen Color-Pro 3F outside to read sunlight, with thin clouds covering most of the sky. It's 4PM daylight saving time here.
Depending on exactly where I pointed the sensor, I got readings from 5780 to 5910. That number would have been lower in direct sunlight.
The CT reading is actually just the ratio of red to blue. The green component of white light is not evaluated at all.
Most modern CT meters include a separate channel to read green and suggest magenta/green filtration to balance it.