Irish recruits had to swear that they were Protestants, but I don't think anyone asked too closely. Ironically, the two Irish regiments – the 18th and 27th – were probably much more choosy than English or Scottish regiments due to their Masonic links if nothing else.
Early in the 18th Century, Irish Catholics were directed towards the Austro-Hungarian army (which was allied with Great Britain) to stop them serving the King's enemies, but large numbers made their way to Spain and France. Relations with officers of the Irish Brigade in French service seem to have been remarkably cordial (when they weren't killing each other).
As GT suggests, from 1778 (during which year the land elements of the Penal Laws were revoked), an attempt was made to draw on this large and previously untapped body. The burgeoning Catholic middle class, keen to prove its loyalty, was heavily involved in raising several regiments of foot in Ireland, with their R&F (and that of the country militias) increasingly being drawn from working class Catholics. During the AWI, a batch of Catholic recruits was sent to America, and the British general Paterson rants on (and on) about them, despising their poor physical appearance and lamenting that the only bad thing about them was that many of them deserted after being kitted out, rather than before. The fact that Paterson was a Lowland Scot is, IMO, significant – you generally don't find English officers talking about them in that way.
After the French Revolution, the British formed the "Brigade Catholique" to accommodate the former Irish Brigade officers and men who defected to avoid The Terror etc. There were at least two Irish regiments that were nicknamed "The Croppies" from the number of former Rebels in their ranks (I think the 87th, which captured an eagle at Barossa, was one of them). Wellington famously used Irish priests and monks in Spain as a key part of his intelligence system.