Not reliably from one simultaneous trigger. While these types of radio triggers can often be used either as a flash trigger or as a shutter remote, firing both at the exact same moment usually won’t sync correctly. The flash is likely to fire before the shutter is actually open.

The reliable method is to let the camera trigger the flash. In practice, that means using one trigger setup as the shutter remote, then having the camera trigger the flashes separately—typically with a transmitter on the camera hot shoe and receivers on the flashes.

If you want remote shutter plus off-camera flash, use a separate transmitter/receiver set for the shutter release and keep the flash triggers on a different radio channel. That way, pressing the remote releases the camera, and when the camera fires, it triggers the flashes at the correct time.

So the switch basically means a receiver is being used for one role or the other at a time, not both simultaneously in a synchronized way.