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I don't think that it would add drag so much as get in the way.
My bike has 6.5" of clearance, and 5.5" of suspension. The inch that's left over is pretty minimal and can be taken up with tire deformation on a big hit. I don't things hanging underneath to get torn off.
The short wheel base and round tires, combined with minimal clearance all contribute to making rear wheel spats unnecessary.
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