Different "ethnic groups" use different ways to define ingroup and outgroup. Language might define it for one group while another it is religion or something like past economic status.
With regards to the Irish, one point in their favour is the fact that their ancestral language seems to be spoken and used to an extent that is not true for a Copt that is close to extinct.
(Note, please, that I do not think that should be the only metric.)
The passage of time is also key. If it is clear that the Irish constitute an ethnic group, it is much less clear for the Cornish, much more assimilated than the Irish. The Cornish language dropped out of use as a community language for nearly two centuries before its late 19th century revival.
I've heard the opposite from a few Copts I know. Groups can have different opinions regarding identity.
Is this debate something like the debate among Maronites over whether or not they, or perhaps the wider Lebanese population, can be considered Arabs?
The answer to that question, and to like questions posed to like groups, is that it honestly depends on the circumstances, including the question of what the people in question prefer. In much of the Arab world, including Egypt, there were Arab and local national identities that were authentically multireligious; in Egypt, the main divide seems not to have been drawn between Muslims and non-Muslims, but rather between natives and immigrants.
Could this have changed? Certainly. I can imagine scenarios in which Egypt might have had a different colonial history, a rather worse one, in which the main dividing line came to be drawn between Muslims and non-Muslims. In that scenario, I can imagine one imperial power or another trying to engage in some demographic reengineering, creating a new concentration of Copts in an area that would be a dependable client state.
(It is also the case that I can imagine an Egypt that evolve rather better, one that did not end up under any kind of colonial control and that became a secure country where European and other immigrants could find a secure place.)