It is a possibility, however they would have various factors mitigating against them. Unlike northern france, Ireland lacked a central administration to deal with or to conquer, yet had kings that, when required like Maelseachlainn Mac Mael Rúnaid, could assemble vast armies to defeat any strong threat of colonisation. Whereas in northern England the killing of one king meant that one could take over the administration of vast amounts of territory, the same could not be said for Ireland, where conquest would have been a much more complicated process.

As for any appreciable change, it would depend on how Sigtrygg was then viewed by his allies after the battle. Remember Brian Bóraimhe, Imperator Scottorum was able to muster just about the same number of men to battle that day as Sigtrygg. Therefore, Sigtrygg had the power of a powerful Irish provincial king for one short moment, captain of an Irish-Sea province. This, I think, could have been the beginning of true Norse contention, in Irish form of course, to the High-Kingship, and they may have focussed their attention on removing certain obstacles, like munster, from the picture. However, it is a rather large what-if.