I would say there is almost certainly a link somewhere because Gay is not a common name and fairly localised in Ireland to the west of Westmeath and later I think to Dublin (going by the 1911 census). Unfortunately I can't confirm this one - at least yet.
My own lineage is:
James Joseph Gay 1923, Mullingar
son of William Gay 1897 and Mary Flood 1900
William Gay 1897
son of John Gay 1851/3 and Anne (Mc)Cormack 1861/66
John Gay 1851/3
son of John Gay and Hannah Whelehan (Anna Whelan).
Unfortunately I can't confirm the parents of my g-g-grandfather John Gay which seems to be about the dates that I'd need to co-ordinate with your records for Peter Gay Wheeler.
I am working on the Griffiths Valuation records at the moment and trying to work forwards as well but this is not fast going!
I will certainly let you know if I come across anything.