On my ST1100, it made things worse. All the air coming up from the bottom forced the hot air out onto my legs.
The 1300 is a different beast, though, so who knows. It seems easy enough to try. Removing the inner fairing panels (those on either side of the radiator) helps, so it's possible removing the entire bottom cowl might help more. Make sure all the fairing parts are well anchored, though, and ride slowly at first. The mounting of the fairing likely wasn't designed with air pressure from the inside out.