This is an odd connection. William Piper, born and married in Hampshire, had two of his children born in Tipperary. A bit of digging (Mary Jane in 1901 census below) revealed that at least one of these was born in Templemore in particular ("Temple Moor"). A Templemore stay in Ireland would appear to rule out any connection with the Pipers from Lorrha and Northern Tipperary. The Templemore C of I records are extant for this period, and record the birth of a Thomas Piper in 1834 to a William and Mary Piper, he being a corporal 67th regt (this was the south Hampshire regiment). It would appear that military service was why this family was in Ireland.
William Piper is given as a french polisher in 1841 census, born Hampshire, as was his wife Mary Fields. Married in Winchester in 1823. Children were:-
1841 census living in Clifton, Bristol
1851 census in Bristol
Note the lodger Frances Monks - I looked at Tipp Heritage Centre results, there is a marriage of a James Monk, RC at Roscrea in 1824, but that means little.
1861 census in Bristol
1871 census in Bristol
1901 census Bristol
I conveyed this to a Geoffrey Piper on Genes, but he chose to dismiss this as "extremely unlikely" as William was a French Polisher in 1841 and could not possibley have been the same man, and he chose to ingore my information and not bother to find out more on the military connection.