Did Wellington consider himself as Irish ?
There is the (apocryphal ? ) quote from him "To be born in a stable would not make me an horse".
98's revolt was more about Irish self-government, by protestant and catholic together, in line with the citizen principle of revolutionary France.
But Wellington family was perhaps more on the opposite side, of establishment more attached to Crown than to country - even if Wellington proposed some reforms, strongly opposed by his pairs.
Some french national figures were born in colonies, where they are not celebrated anymore: e.g. general Juin, born in Annaba and leader of the french corps in Italian campaign 1943-44, quite forgotten in Algeria.
Motivation of irish soldiers, so numerous in all british regiments, is what french historians call a "memory stakes" : in a time where catholics were officialy discriminated, and massively in the poorest part of the society, were they motivated by a kind of partriotism/loyalism, or by the enlistlment bonus, like soldiers of Ancien régime ?
A sensitive question about the place of Ireland in UK triumph in 1815, which can trigger bitter arguments even today.