The answer here is uncertain. The Varangian are not hugely frequent in Byzantine sources, they were a bodyguard force and their deployment to the field armies even in the Middle Epoch period c.1050 is often more notable for their presence than any mention of an organised body.

Niketas Choniates and other witnesses to the Fall of Constantinople in 1204 talk of Varangians defending the city walls. Indeed, the emperors Alexios III/IV are criticised for withdrawing them from the points at which the Venetians were attacking the Sea Walls to defend the castle. Choniates believed the τάγμα των Βάραγγων alone could have repelled the invaders. It's rhetoric written in hindsight but still interesting.

After 1204 the empire is diluted and scattered, the regiment as it was is hard to find, not least because there were now four different men claiming to be Βασιλεύς των Ρωμαίων, all hiring mercenaries. Nicaea particularly under John Vatatzes had a sizeable Latin mercenary force (See Akropolites) but references to the norsemen get less frequent.

My specialisation is the later Komnenoi period but to the best of my knowledge the bodyguards of the Palaiologan emperors were Latin as the viking era had largely passed and Russia had its own struggles with the Golden Horde. This was surely only compounded by the fact that Constantinople never regained the wealth it had before. We know from the accounts of Russian Pilgrims to the city c.1200 (See Majeska, Russian Pilgrims in Constantinople) that's they had a specifically russian church used by varangian members but I don't know of later reference to it. If the church fell out of use and was not maintained it is a sign that the once heavy stream of axe wielding warriors had become an trickle.

If you're interested we do possess a full register of the foreign defenders of the city in 1453, including one Scotsman, so have a search within. You might find a few descendants.