Was Shakespeare Irish?

In the last scene of Hamlet's first act, the prince swears by "Saint Patrick," (1.5.141), which seems an odd thing for a medieval Dane to do. Could the man who created Hamlet have been Irish? Now that's a conspiracy theory worth believing.

Sanctuary of Saint Patrick
on Station Island in Lough Derg
(County Donegal, Ireland)
Alas, Shakespeare has Hamlet swear by Patrick because the saint was supposed to have been the keeper of Purgatory, where Hamlet's father is confined during the day. A legend about St. Patrick, less familiar than his chasing the snakes out of Ireland, says that Jesus showed him the entrance to purgatory on Station Island in Lough Derg (County Donegal). The island remains a pilgrimage site to this day.