Its possible that some modern Polish people have some mongol inside them, it's also possible that the lochness monster exists.
That some modern Polish people are descended from member of the Golden Horde is not only possible it is an accepted fact. A Lithuanian grand duke named Witold, who was the cousin of the first Lithuanian king of Poland, was a backer of the Golden Horde in its struggle with the forces of Tamerlane, and when Tamerlane defeated the Golden Horde this grand duke allowed the members of the Golden Horde that survived the defeat to settle in Lithuania. The following is from an article by Dr. Marzena Godzińska titled "Polish Tartars":
The beginnings of the Tatar settlement in the Grand Duchy of Lithuania occurred in the 14th and early 15th centuries, but especially during the reign of Grand Duke Witold, the cousin of the Polish king, Wladislaw Jagiello. From the second half of the 14th century, power struggles began to arise in the Golden Horde that had developed from the clan of Jochi (Czyngyz Khan's eldest son.) Pretenders to the Khan's throne often came to solicit the support of Lithuania, or, with their families and followers seek asylum within its boundaries.
Today, the majority of the descendants of Tatar families in Poland can trace their descent from the noble status of the early Polish-Lithuanian Commonwealth.
From the beginning of the 15th century, the Tatar army participated in all of the wars of the Polish-Lithuanian state. They began their struggles in the Great War against the Teutonic Order in the years 1409-1410. At that time it was a very war of survival for Poland and Lithuania and, to the present day, the victory at the Battle of Grunwald is one of the basic elements of historical consciousness for all Poles, including those of Tatar descent.
One illustrious Pole descended from Tartars is Poland's first Nobel Literature Lauriate Henryk Sienkiewicz: