My understanding of it- especially as it relates to gumwall bicycle tires- is that the main purpose of the "rubber" is to protect the cords. I've had gumwalls so weatherchecked the gum came off in chunks but the tire still held air.
P.S.
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Once the fabric has been woven between the beads, and the tire has its basic shape, it is coated with rubber. The rubber is mainly there to protect the fabric from damage, and has no structural importance.
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http://sheldonbrown.com/tires.html