"Looking at the Nicosia line-up last night, it looks like all but 2 of the starting 11 were actually Cypriots."
According to their wiki page, eleven of their twenty-seven man squad are from Cyprus. I looked back at the team that lined up in the last CL group game, and three of these eleven started. Of the other eight of the starting eleven, five were Brazilian and three were Portugeuse. It does suggest a purchasing power beyond Irish clubs.
APOEL also effectively represent Greek Cypriots (the acronym stands for "Athletic Football Club of Greeks of Nicosia") and even the most cursory knowledge of their history suggests they can then draw on supporter identity in a way that no LoI club can.
There's no doubt they are punching above their weight, but I don't think its likely that any other Cypriot club will emulate their achievement, nor do I expect them to reproduce it regularly. It's hard to see them as a model for LoI clubs to follow. I'm open to correction as I have a fairly slight knowledge of them, but at first glance...