Of course, your glide ratio would improve noticeably. Technically, since the drivewell is forward of the center of lateral resistance, it would track slightly better. Whether you would notice it is another matter.
You should get pretty good tracking with the rudder down and neutral (where it acts as a skeg) and make small heading corrections by tilting the hull slightly away.
If you knew ahead of time that you were paddling exclusively, you could tape up the seam to streamline the hull bottom -- the plug could even be omitted in that case (slit the tape if you need to drain through the well):
I do this on to the front cockpit on the tandem when going solo -- works great!
