As it happens, there is no actual evidence that even a majority of NI catholics would support unification if it came to a referendum.
What evidence there is points pretty firmly in the other direction, actually.
It's a myriad really. The problem is that Northern Irish and Irish identity is interchangable. The two political outcomes are a result of a divergence in opinion as to Ireland's future. Catholics certainly don't feel 'British.' In comparison Catholics in Scotland do tend to identify strongly Scottish over 'British' but are traditionally 'unionist' (but not 'Unionist') as remaining in the UK was preferrable to the alternative of independence. For most of the last century Scottish independence would have manifested itself as a Presbyterian non-secular hegemony; a Northern Ireland Mark II. Of course, Scotland has rapidly secularised (it could be argued more so than England and Wales)
While re-unification has romantic appeal to some Catholics in Northern Ireland, the suspension of Home Rule and the introduction of an army presence was initially welcomed as a protection against political Orangism. Even during the 'Troubles' it was more welcomed than perhaps many Catholics would care to admit (and always preferable to the police)