No. Wingtip strobes meet all requirements, and the tail strobe you have is ... a nice addition.
'53 B-model N146YS SN:25713
50th Anniversary of Flight Model. Winner-Best Original 170B, 100th Anniversary of Flight Convention. An originality nut (mostly) for the right reasons.
I believe there are visibility requirements the wing tip strobes must meet and therefore the tail strobe may be required to complete those requirements. If your stobe system meets those requirements then you don't need the anti-collision light. Jon
Look at the Whelen section in a Spruce or Univair catalog, there's a drawing showing the strobe coverage/visibility. I believe that the wingtip strobes alone (piggyback style onto the position lights) meets the requirements.