Short answer is "No."
As far as practical considerations go, there is little savings in a 3-engine taxi with the APU running. Also, you have to consider whether you will have a clear path behind you for a crossbleed start (likely prohibited while taxiing), or will be taxiing long enough to make a difference before restart, before you shut down the APU.
FOD is always a consideration if you will have to use more than idle thrust, not to mention negating much of the fuel savings.