What sort of history do you mean? I presume you don't mean that our predecessors suddenly appeared in Poland from the moon in 966 and immediately accepted Christianity (or perhaps had Christianity foisted upon them for political reasons). Do you mean written history? Then yes it begins with 'that guy' (his name was inter alia Mieszko) - specifically the excerpts of the account of ibn Yacoub relating to his journeys in 961-962. They describe a well-established state but say nothing AFAIK about its religion. So clearly, written history does not begin in 966 nor is it related to Christianisation.
This would be a much more convincing argument if the date itself, the circumstances of the event and at least 50 -150 years after were not themselves a 'black hole' of 'invented legends'. All we can be reasonably sure of is that most likely between 960 and 975 Christianity became the state religion of what was later to become Poland and that Mieszko was the ruler at the time.Christianity in 966. Earlier, we have a black hole where much later invented legends slowly levitate.
As this statement is patently absurd, I can only presume you mean it as a hyperbole. However, while pre-Christian history may be meaningless to you, that is a view which is not necessarily shared by others. I would suggest that ignoring everything that went before the imposition of ones preferred system of beliefs is a poor substitute for holistic assessment when we attempt to assess a culture. The point is that one can, for example, declare that Poland's history began in 1946 with the creation of the Polish People's Republic and that there was no Polish history before then and that, therefore, all Polish culture has always been based on communism. It is just as absurd and just as likely to lead to wholly incorrect conclusions.There is no such thing as pre-Christian Polish history.
It does however suggest (quite strongly in my view) that Polish culture was different to that of the vast majority of other Christian cultures. It also proves, among many other pieces of evidence, that there were many influences on Polish culture other than Catholicism. In this instance a very strong humanist influence.That the Commonwealth was tolerant doesn't prove that today Polish culture isn't based on Catholicism.
This would be a stronger argument if you weren't citing 966 as the starting point of Polish history and evidence that Polish culture was 'always' based on Catholicism. Also, if proximity to modern times is to be the determinant for being the basis of culture, then Communism has a much stronger claim to be the basis of modern Polish culture. Incidentally, just how representative was the opposite view to that of the Warsaw Confederacy of 1573?The (unrepresentative) Warsaw Confederation happened almost half a millennium ago.
The point is that, in my opinion at least, Polish culture is the mainstream and not a branch of Catholicism. Modern-day Polish culture is based on previous Polish culture, which existed long before Christianity became the state religion of the Polish state. However strong, Catholicism is but one of many inputs into that mainstream but not the mainstream itself.