Most "pros" (whatever that means these days is up for debate!) use Manual mode for all flash photography. When shooting flash pictures, I would say that 99.5% of the time, the best choice is to have the camera in M mode, with a set shutter speed, and a set, pre-determined f/stop. Due to the way flash works, Manual exposure control is normally the most logical,safest,most-predictable mode to shoot in.
I would say that as far as regular work, most pros use manual mode a lot, but a lot of pros use aperture priority automatic, which Canon calls Av, for Aperture value. This mode is very fast, and it's easy to look at the settings in the viewfinder, to keep an eye on things. It also works great with +/- Exposure Compensation (also called EC) dialed in.
There's a segment of new pros who rely on the newer cameras that have superb sensor performance, and who use AUTO ISO exposure setting combined with +/- EC to get the right exposure parameters for BOTH the shutter, and the f/stop, as well as keeping the image well exposed despite rapidly-changing backgrounds; this is becoming a new way to shoot things like wildlife and action.
There are some times when the specific, exact shutter speed is the number one parameter for successful results, and using Tv or Time value (Shutter Priority auto) can be a smart option.
The key is to use the RIGHT mode for the task at hand, and not to be too ignorant or stubborn or dumb to be fixated on one,specific way to accomplish the task.