This is a complex question to answer.
In short, no the dative is not used, except by some speakers in Munsters. However in many dialects the historical dative form is actually used as the nominative form.
The Caighdeán however gives about 7-10 words (don't remember exactly how many) that one must use the dative with.
Complicating things even further however, native speakers don't really say Éire, but Éirinn.
"In Éirinn" is also used as an intensifier:
Ritheas chomh tapaidh in Éirinn agus ab fhéidir liom = I ran as fast as I could.
Ritheas = Rith mé
An interesting question. There are cases, particularly with placenames, where the nominative has been replaced completely with the Dative (e.g. Corcaigh=Cork). The word Treabh (Tribe) has now been replaced by its Dative form 'Treibh' and its grammar altered to reflect that fact, so that a road in Galway 'Bóthar na dTreabh' should technically be called Bóthar na dTreibheanna. I sincerely hope that that does not happen. Some feminine nouns have retained their dative forms, particularly those relating to body parts (2nd dec).