Is it safe to screw #14 screws into the bottom of Center Support Beam?
This will be absolutely fine. People put screws into beams all the time. The fibers that run along the beam will barely be broken by this. (Notches out of the beam interrupt the fibers, which makes them another story altogether.)

You might want to predrill with a small (like 1/8") drill bit to make your life a little easier.