The attacks I'm aware of use processor timings to measure the effects their programs are having. However, because an asynchronous circuit doesn't complete tasks in a reliable cycle, you can't measure how the pipeline is being effected by your program in the same way. You could find new ways to force the processor to act in a reliable manner that you could measure, but that may change quite randomly from processor to processor, or even from moment to moment, depending on external environmental factors.