No, not the north star. But there is PLENTY of evidence for conjunctions of of Saturn and Jupiter and the star Regulus, and three c planetary conjunctions in one year, including with Venus, but NONE of them with the north star, either Polaris or whatever star was the north star 2000 years ago and maybe Venus as well in the years around when Jesus was born.
The north star was NOT part of the conjunctions.
"...In the Babylonian system Jupiter represented the star of Marduk, the supreme Babylonian god. Saturn was the "Steady One." The constellation Pisces was associated with Ea, the god of wisdom, life and creation. The conjunction of Jupiter and Saturn in Pisces predicts from Babylonian's viewpoint "the end of the old world order and the birth of a new king chosen by God." Parpola contends that Augustus' (BC 27 - AD 12 or 14) authority was still questioned and there was power vacuum in the Middle East, and the people, including the Jews, were looking for a new King that would topple the Roman Empire.
Here are the dates of three conjunctions in 7 BC according to Parpola.
First conjunction: May 27, 8am
Second conjunction: October 6, 10 pm
Third conjunction: December 1, 9pm.
The triple conjunction is rare, occurring every 800 years. Since 7BC, triple conjunctions were observed in 786 and 1583.
According to the UB,
First conjunction: May 29.
Second conjunction: September 29
Third conjunction: December 5.
Thus, there are some discrepancies of the actual conjunction dates that are recorded in the UB and those proposed by Parpola, although they are fairly close. There are some software which can be used to track the movements of planets in any year, including 7 BC, and someone presented these conjunctions at the Foundation a year ago. However, I was not sure if these computer programs calculate the dates using Julian calendar or Gregorian calendar.
The above discrepancies may have to do with the difference in Julian and Gregorian calendars or some glitches in the computer program Parpola used. If it is the latter, some smart readers could calibrate and write an article to pinpoint the correct time and dates of the triple conjunction, correcting Porpola's errors. Even if there were minor errors, I think it is significant that a prominent biblical scholars proposed and accepted unwittingly one of the important scientific event described in the UB...."
http://www.public.iastate.edu/~lightandlife/triple.htm
"...huban was the Pole Star some 5,000 years ago, when the Egyptians were building the pyramids.
The Great Pyramid of Giza, an enduring monument of ancient Egypt. Egyptologists believe that it was built as a tomb for fourth dynasty Egyptian Pharaoh Khufu around 2560 BC.Image via Nina Aldin Thune/Wikimedia Commons.
Thuban is not a particularly bright star, but it holds a special place in the hearts of stargazers. That’s because Thuban was the Pole Star some 5,000 years ago, when the Egyptians were building the pyramids. follow the links below to learn more about Thuban, now a relatively inconspicuous star in the constellation Draco the Dragon.
What is Thuban’s connection with the pyramids of Egypt?..."
http://earthsky.org/brightest-stars/thuban-past-north-star
AND , FYI Polaris is NOT a very bright star,. Vega is NOT the north star.