It's a bit complicated, actually. The Olympics features "Great Britain" and "Ireland", rather than "United Kingdom" and "Republic of Ireland", so Northern Irish athletes can participate on either. Sometimes this is based on national identification, but a lot of the time it depends on whether or not that sport happens to be organised on an "all-Ireland" basis.
The trick there is that "Spanish" implies identification with the Spanish national identity in a way which "British" and "North American" typically do not (or in the British case, at least, not necessarily), so Catalan separatists are unlikely to identify as such. The politically-neutral, simply regional term would be "Iberian", i.e. including Portugal alongside Castile, Catalonia and the rest, in much the same way that "Scandinavian" includes Swedes, Danes and Norwegians, without implying shared nationality identity.
Of course, as you say, most Catalonians are legally Spanish, but many of them are legally French or Andorran, so that's a claim about individual Catalans, not on collective identities.