If the Celts island hopped from the Shetlands to the Faeroe Islands then they could hop onto Iceland. The catch is that apparently the Faeroes were out of reach of pre Viking ships.
Also apparently Iceland was known to Ancient Greek geographers...
You don't need cities,; an agrarian population would do fine. The only trouble is that they will trash the environment as the Vikings did.So if you can get the Irish to get the knowledge of city building from somewhere else than the vikings there is no reason why they would not flourish and be forced to settle abroad.