This is linked to the time when the mongols attacked Europe.
There is no historical evidence for this. The invading force was minuscule in comparison to the rest of the population. What did happen however was the migration of some Tatars to the country over a period of time to serve in the army, these people have long since integrated into the Polish population. Furthermore in recent history the Russians always stained quite big armies in Poland going back to some 200 years, that usually numbered some 100 000-150 000, it is quite plausible that some Poles might be the descendants of those Russians. The second proposition is just speculation, but it is far more probable than your hypothesis.