James Merryweather (quite an authority on early music) recently commented:"Bagpipes have contributed to music making for a very long time, possibly (probably?) originating in the countries around the Mediterranean, it can be reasonably estimated, more than two thousand years ago. It has been said that the Romans had a bagpipe, perhaps the instrument played by Nero, who perhaps piped rather than fiddled as Rome burned. That there was an early Italian bagpipe is not unlikely, although little of any worth has ever been published to support the idea. Even so, over-optimistic authors have extrapolated some very flimsy data to support a theory that the Romans ("therefore") introduced the bagpipe into the British Isles...-James Merryweather, Regional Bagpipes: History or Bunk? (EFDSS Members' Newsletter, vol. 64 no. 2, Summer 2002).As far as we can tell, the bagpipe was not in common use in Northern Europe until the thirteenth century, when its existence in various forms may be inferred from its occurence in art."
All we can reasonably say is that it is not impossible that some form of bagpipe was known in Britain in what we take to be the Arthurian period; that doesn't mean that it is likely.