Does th place in Ireland called limerick relate to the poem?

I'm not positive, but it MIGHT have some minor connections :)

NO

Wikipedia says the connection is tenuous. The possible connection comes from a one time "parlour game" in which "Follow me up to Limerick" comes at the end of some foolery. Limneach which is the Gaelic name for Limerick, literally means the "limit".. dead end.

In an extract from an essay on the 'Form and Prehistory' of the Limerick, Marco Graziosi says "According to the Oxford English Dictionary, the term "limerick" first appeared in 1896 in two letters by A. Beardsley ("I have tried to amuse myself by writing limericks on my troubles", 1 May; "Your continuation of the limerick is superb", 2 May). After discussing other claimed origins of the name he goes on to say "we are therefore left with the traditional association of the term with the Irish city, according to the OED:
Said to be from a custom at convivial parties, according to which each member sang an extemporized 'nonsense-verse', which was followed by a chorus containing the words 'Will you come up to Limerick?'

It does not...