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The rear axle mostly moves up and down, due to the location of the pivot, and the range of suspension travel is pretty limited. Due to the fact that the rear axle travels in an arc rather than just up and down there is some alteration in chain length due to suspension movement, but it's tiny. If you ran with the chain really, really tight then I suppose it might cause issues, but it's well within the limits of a reasonably slack chain to take up the fore-aft movement caused by the suspension.
I must have miss this, but what about the suspension block?