You would have to make the support tube a very large diameter to insure the gaiter never touches it. Unfortunately the thing can billow out like a baloon when full with water.
You could however install the gaiter on the autopilot tiller arm instead. Make a second piece for the shown support tube with a slit for the autopilot tiller surrounded by a round or oval flange. The tiller would need a round collar for the gaiter to seal around. The second piece of the support tube is sealed against the first one either by screws and sika, or you can permanently glue it in. This obviously depends on how you plan to attach the autopilot tiller to the rudder shaft (wich is another can of worms if the shaft is hollow).
Me I would take a simpler route, put a full bulkhead centered on the rudder tube, cut a big round hole where the autopilot tiller goes, add two knees to support the lower tube longitudinally. The upper remains of the original rudder tube don't neceserally need longitudinal support, but if it makes you happy you can also add to knees there.
I know, tabbing everything in would be a pain, but the end result is much stronger then even what's there now.