Erik XIV of Sweden had the idea in 1566 that his oldest daughter from his first marriage, Virginia, should be married to Tsarevich Ivan Ivanovich, son of Ivan IV. From what I have read, Erik XIV was considering an alliance with Russia and was in a seven-years truce with them as of 1564. However, Erik XIV was eventually deposed and his half-brother took the throne in 1568.
The conversation that I am currently engaged in involves a surviving Isabella (1564-1566), first daughter of John III. After doing a bit more reading, I found that his surviving daughter, Anna (1568-1625), was the subject of a false rumor involving a marriage to Tsar Dmitri (False Dmitri I). Anna never married in OTL.
What is the likelihood of a marriage between a member of the house of Rurik and a member of the house of Vasa? Despite the rumors, there were daughters from the Swedish royal house that could, theoretically, be married to a tsarevich. In addition, what are some potential effects of a marriage between these two houses?