If they say they want a credit check then I think you will need to provide one. Your nationality is not as relevant as the fact that you are living abroad and could in theory be up to your eyes in debt for all they know.
I looked into the same thing a few years ago, in my initial conversation with AIB they were only looking for a tax return from the country I was living in. I didn’t go through with it but I don’t recall a credit check being mentioned. Still, that was “the good old days” so this may be a new requirement.
So, long story short, I think the answer is yes, but you will have to be prepared to jump through the hoops.
I looked into this quite a few years ago (at the end of the boom). AIB said that I could get mortgage as long as I had a 20% deposit (if I remember correctly). I was essentially being treated as a Buy to Let buyer.
As to the foreign credit check. AIB are looking for them now. Don’t know if it’s a problem for you but as someone who lived in UK for a while it wasn’t a problem for me. Just got one for £2 through Experian. AIB accepted it. Different country I know.
I live abroad and have been approved for a mortgage by both AIB and B of I. AIB have asked me for a credit check but I haven’t done this yet so I don’t know what it entails in terms of time or cost. Has anyone jumped through this hoop?