It's likely that there had been a significant amount of cross-fertilisation of both cultures.
If anything, the Picts would have been undergoing some degree of Gaelicization long before any 'Dal Riadan takeover', with the Columban Church spreading Irish culture throughout Pictland for hundreds of years beforehand.
Likewise, the Kingdom of Alba is referred to as 'the kingdom of the Picts' long after Cináed mac Ailpin's death, so it seems as if the Dal Riadans (if that's what the mac Ailpins were) maintained significant elements of Pictish social organisation.
Looking at the Pictish kinglists, there seem to be quite a few demonstrably 'Irish' names well in advance of the mac Ailpin takeover. Likewise, wherever the mac Ailpin dynasty originated in the male line, it would make sense if there was a female Pictish inheritance that made a claim on both thrones viable.
I guess the scenario depends on what you believed actually happened as the kingdom of the Picts came to an end. There's so little evidence, that you're effectively working with educated guesses and hypothetical arguments drawn up by scholars centuries after the event.
A not inconsiderable body of thought states that Cináed mac Ailpin was, in fact, a Pict himself, and that the Gaelicisation that happened after his accession was more related to the education of Pictish aristocrats in Gaelic-speaking monasteries than anything else. If you want Pictish culture to survive, remove or weaken Columban Christianity and replace it with Orthodox catholicism (as King Nechtan attempted to do in the 700s).
The traditional school of thought states that Cináed seized power after the decimation of the Pictish ruling class in battles with the Viking hordes. In which case, offer a more favourable history and have the main Pictish royal line(s) survive these trials.
They could pursue a diplomatic policy with the Scots, leading to an eventual 'anschluss' at some later date, as the Scots seem to have been getting the works from the Vikings at around the same time. The two peoples had a lot in common, and a union based on a more favourable Pictish negotiating position might well see a Pictish-speaking aristocracy taking control rather than a Gaelic one. This united power would be a force to be reckoned with, and would form the analogue to OTL Scotland.
There will be some centralisation: it seems to have been the trend in Northern Europe at the time. You might initially have a Pictish High King ruling over his own domains in the north and east of OTL Scotland, with nominal authority over a Dal Riadan sub King, a sub-king of Strathcylyde, and whatever odds and sods he manages to haul away from Northumbria in the Lothians and the Vikings in the north. Whether he could forge that into a united, Pictish speaking nation, however, is very open to debate.
Linguistically.... well, the country will be completely different. We have no idea what Pictish sounded like, but it's likely that it was Brythonic-ish, so the modern day 'Scots' might sound more like the Welsh. The butterflies would be immense.
I might even by typing this at my desk covered in tatoos of weird animals and geometric shapes, supping my heather ale and thinking about what designs to add to my latest standing stone
