I don't think so. My understanding was "confirmed" by ChatGPT, though I haven't looked at the sources.
> Rugby in Ireland is governed by the Irish Rugby Football Union (IRFU), which was established in 1879, decades before Ireland was partitioned in 1921. It has always organised rugby on an all-Ireland basis.
Oh! I looked into it more and you're quite right that the IRFU decides and their rule happens to be about the island of Ireland and so who may control some or all of the island is irrelevant. Thanks.