On one hand, to broadly presume that a Normanless England is a net positive in all things (to include being less hostile/aggressive to its neighbors) is fallacious and fraught with hyperbolic utopianism that has no place anywhere...and I say that as a general Norman naysayer myself. A country in that timeframe with any pretense to influence would be one prone to warfare in some shape, and I don't see that not holding true with the Celtic lands in the British Isles, with or without the Normans. All it could take is one king with a particular axe to grind against Pick A Celtic Country and decide they've had enough (looking at you, Alba).
HOWEVER, it's equally important to keep in mind that there exists no well-documented case of hostile aggression on any large scale by the Anglo-Saxons (pre or post unification of England) against either Ireland or "Scotland" (insofar as Scotland wasn't really around in the form we know it), and that even Anglo-Irish/Scottish warfare post-1066 was intermittent until Henry VIII's rule in the 16th Century, with the Statutes of Kilkenny not coming about until three centuries post-Conquest*...that's a long time and several dynasties removed from the Old English period. Certainly too far to accurately or fairly 'pre-date' later English oppression against Gaelic peoples rearward in time to the AS period.
Even Anglo-Welsh relations don't really prove anything, as "Wales" wasn't a unified polity pre-1066 but a collection of kingdoms, generally under an over-kingdom like Gwynedd or Powys, that had as much of a tradition of allying with Anglo-Saxon kingdoms as fighting them (shoddy/politically motivated historiography be-damned), especially against the pagan Northmen. That combined with archeological evidence failing to bear out claims of widespread massacres of Britons during the settlement period (and a common use by Anglo-Saxon kings of rather Brythonic names) seems to undermine allegations that the English wiped out native Celts in lands they came to inhabit.
*Fans of historical determinism like to trot this little gem out, but it's worth remembering that Kilkenny was a failure, and Lionel Duke of Clarence ended up taking his ball and going home rather than pushing home any effort to quash Gaelic influence/culture. Meanwhile, Ireland stayed just as Gaelic as before for the next two hundred-odd years.