Sorry, but that simply isnt true.
From what I have read, Pictish DNA has and is turning up.
And the Picts were a physically strong race, who wouldnt have totally succumbed to any plague. A plague which there is no evidence happended in what is today Scotland at all, either Pictland, Dalriada, Strathclyde or even the celtic kingdom in Galloway, which faces the north of Ireland, sitting as it does in the far south-west of Scotland.
Also the Plague was in the mid 6th century. And the Pictish kingdom in Scotland existed until the mid 9th century, when Pictland and Dalriada became joined under the rule of King Kenneth McAlpine in 843, a king whose ascension was due to the matrilinear Pictish line.
Far from disappearing in 541 or so, the Picts were a strong and thriving ancient kingdom for another 300 years!.
Re the Irish Celts, I again refer you to the remarks and evidence I last posted, which shows that the Dalradic (Irish) influx is now believed, through the latest archeology in Argyllshire and Western Scotland, allied to evidence uncovered in N Ireland, to have been much smaller than believed.
Re the Irish slaves, the heaviest concentration of ‘Norse Gael’ or Norse DNA in Scotland will of course be in the areas that we know were invaded and partly-colonised (either by force or peaceful intermarriage), such as Galloway in the S/W, the West Coast of Scotland from the Southern Highlands northward, areas of the North and North East, areas in the far S/E where Bernicia existed, now the Eastern Borders.
There were huge areas however where the Vikings did not successfully plant their DNA and failed to successfully invade: the kingdom of Strathclyde (modern day north west of Glasgow to South Ayrshire & Lanarkshire, the Western and Central Borders)and of course most of Pictland (which was most of the Highlands).
Re Indo-European:
I can remember being taught in my ‘Higher’ History class at secondary school (your senior High School) that four European languages were not I-E: Basque, Pictish, Finnish and Hungarian.
During the plague in the 1300s it was noted by many that as it moved North the death rate dropped, and by the time it got to Northern Scandinavia it was down to 10%.
The Plague of Justinian was not reported to have moderated, and although news reports from that time are few and far between, it was entirely possible that it simply killed off everybody it could infect ~ leaving behind a population remarkably immune to the plague.
I know there's this "need" many feel for the Picts to have made it through the Dark Ages, but they may not have made it TO the Dark Ages.
There was a reason for Scotland to be so open and attractive to newcomers ~ there was no one home!
There's another non IE language you need to know about. It's called Estonian. It really is different from Hungarian and Finnish ~ at least its speakers say so.
The closest ancient language cognate to the Sa'ami languages is called Sumerian, and it, in turn appears to have originated among the Dravidians. Lots of history in that one just now being discovered.