Fairly plausible, especially if the goal is to replace the Circassians Russia genocided.
In OTL the settlers from the Balkans had been invited in the XVIII into the newly conquered lands of Novorossia. This was relatively easy because the territory (Wild Steppe) was pretty much empty. This was nothing like situation on the Caucasus where the agricultural territories had a relatively dense sedentary population.
As far as the goal you mentioned (avoidance of genocide) is involved, it is a noble one but you are talking about the XIX century when the imperial powers did not care too much about the methods used to deal with the “natives” so the motivation seems to be a little bit anachronistic. Then, again, why would the Circassians voluntarily leave their ancestral lands? Just because the Ottomans said so? They did not acknowledge the Sultan’s authority except in his Caliph’s capacity.
In this specific case,
from the Russian imperial perspective, there was a
hated long-term enemy, which did not fully capitulate (at least as far as AII was concerned), was acting (or could be acting) as something of a fifth column during the CW (*) and, among many other “sins”, was living on the good agricultural lands that could be granted to the loyal Cossacks of the Kuban. Tradition of dealing harshly with the “uncivilized opponents” was there (for example, in the 1780s the Nogais had been forced to flee from the Black Sea steppes to the Caucasus and most of them eventually fled to the OE, the process continued all the way to the 1860s so out of 1 200 000 in 1774, by the late XIX their numbers in the RE were in the low tens of thousands, pretty much the same goes for the Tatars of Crimea) for well over the century so this was nothing new except for the scale. This is not an apology of the practice, just putting things into the historic framework. On the other side of the equation was the OE, which also took an advantage of the situation mistreating the refugees.
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(*) They most probably did not on any serious scale but Palmerston’s idea of creating “Kingdom of Circassia” helped to create this perception. However, the mutual hate did exist on both sides: what could one expect after at least a century of never-ending border war?