No. If you are going that route, make Ireland start as the junior partner under England with just the one province actually controlled.
The idea of what would be, at most, a county level title in Ireland being considered a PU to England while the substantial French titles are assumed to be wholly subsumed into England is silly.
The legal idea was they were Kings of Ireland due to papal sanction, but that Ireland was a separate kingdom. This is significantly different to the status of Wales which was nominally annexed into the kingdom of England much earlier. That legal theory lasted almost to the end of the game period, when Grattans Parliament approved the Act of Union.
Honestly, if we look at how fast Ireland gets absorbed, making it a PU might actually make it last longer, and could allow for the occasional “break free” scenario more often than the current setup. It might require some revision to the ideas for Ireland though, as they would really need to loose the “Irish republicanism” flavour as that would make no sense.
The current set up isn’t that bad though, once you allow for the pragmatic realities of the game.