While maybe more can be said and it was a while ago, this question was also addressed on /r/AskHistorians some time ago. It was answered by /u/gamberro who said that:

As the article you link to suggests, it does appear that sucking nipples was a means to pledge loyalty in pre-Christian Ireland. Saint Patrick mentions in his Confessio that when he fled Ireland, he was offered passage on a boat by some sailors, although he refused to suck their nipples. Interestingly, Patrick considers this to be a barbarian custom and that he refused "for fear of God."

Here is the relevant translation of the text. This translation here prefers the term "breast", but I think it's clear that the general idea was that this symbolised submission and loyalty to another. I can't read Latin unfortunately, but somebody else could shed more light on whether this is an accurate translation.

A now deleted account chips in and says that "I've never found any reference to this practice outside of Patrick's Confessions". Other commenter /u/AxelShoes also didn't find other sources of the claims that this was a thing.

It has been 9 years since that post and maybe more it so be said now by others that know more about early-Irish history. Most recent (pop)articles I can find though all refer to the writing of Patrick and simply extrapolate from there without any additional sources.