Norse influence definitely predated Scots Gaelic. Moreover, the Kingdom of Dal Riata doesn’t seem to have overlapped significantly with early Viking settlements in the Isles, North and East. Though there was competition between them & Dal Riata and of course, the Pictish people who predominated in other areas of Scotland. And of course, the Kingdom of Northumbria.
There was no linguistic monopoly particularly until much nearer the 10th or 11th century when Gaelic became widely used. Vikings were active in Scotland from 8th Century. Even Highland influences on modern English can sound like Scandinavian languages with a unique ‘lilt’ and ‘intonation’ less common in other parts of Scotland.
Scotland’s linguistic ‘mess’ is fascinating, though one wonders what happened to Pictish and what mechanisms drove people to start speaking Gaelic so broadly in the 9th Century. Did it suggest some rising political aspirations? Economic realities? Or simply the end of the post-Roman period?
I doubt that Scotland ever had a monolingual environment at any point in its history, but Gaelic and various Englishes have come close.