Clare --
I think the answer to your questions is: It's not a stereotype; more like a nation-biased joke. You're in England; England has been the enemy of Ireland for centuries.
In fact, I've heard the same joke, only it was applied to Polish people.
Strange; the only Polish people I've met have been plenty smart. The priest where I grew up was Polish and knew several languages.
The FACTS are that Irish folk are above-average intelligent (assuming they don't vitiate their advantage with too much alcohol). A disproportionate number of priests and missionaries were Irish (in the Fifties, for example). And back then, you had to learn more languages than just Latin to graduate from the Seminary. I'm sure we can all agree that becoming a priest takes some serious mental ability.
So A) it's not a stereotype, strictly speaking, but more like wishful thinking :)
and B) it's not widespread or pervasive, being held ONLY among the population of a country's main rival.
I think if any belief/stereotype is only held by a country's rival, we can rule out any truth :)