I'd say that the first caused the second. Meaning that Rome had to either conquer Ireland, or leave the Britons in what is now Wales enough of their ancient tribal structures, and enough personal pride, and enough arms, to protect themselves from Irish raiders. Rome could not reduce them to sullen, unorganized, unarmed, sheep, as it did to the inhabitants in most of the Western Empire, without first eliminating the Irish wolves just to the West.
But Rome did conquer them, although it did not oppress them to the same extent it did in the areas of Britain nearest Gual. The oldest continuously existing Christian community in the British Isles is in Wales. The very name "Wales" comes from the name for foreigner that the Germanic barbarians gave to to people and things assciated with Rome. Wallonia, Wallachia, Vlach, walnut and Wales all derive from the same Germanic root word, because the Germanic invaders of Britain associated the Christian people of what we now call Wales, whose priests and ruling class could speak Latin, with Rome.
Take that Germanic "filter" out and you are looking at the word "gaul", "gol" (as used by the Greeks in "Magolis" ~ "McWallace" ~ ally to Carthage in the Punic wars), "wal", "alle", "Wall" as in Walonia", and so on.
I think it's a pre-Gaellic word meaning something like "spear chucker". Caesar certainly thought so ~