I firmly believe Poland has a MUCH different experience in WW2 with Pilsudski around.
I agree. Had Pilsudski still been head of state of Poland before and during WW2, I think the sheer force of his personality and his prestige could have caused different paths to have been taken in the crucial stages of WW2 that ultimately effected Poland.
No doubt Pilsudski's presence would have solidified the London Government and I'm fairly confident the liberties HMG took with the Poles would not have occurred. Whether for good or bad, Pilsudski, when ascertaining the depth and perfidy of HMG's betrayal, would have cancelled Polish support of the Allied war effort and focussed attention on Poland fighting for Poland's freedom, rather than someone else's, and with no prospect of support in kind.
Teheran would not have occurred because Pilsudski would not have let it occur. He would have demanded to be present or to have it made known what were the terms of the agreement in principle reached between the Powers there. If Poland was treated as an unpaid wh*re by the Allies, Pilsudski, at the very least, would have been the pimp beating down doors demanding payment and recognition for services rendered.
The Promethean principle promulgated by Pilsudski too could have gained better purchase just prior to the commencement of WW2. Whilst it engendered some revulsion, it was inherently sound and a common sense proposal for that region of Europe at that time, having regard to the fact that the region was bordered by two of the most bloodthirsty regimes in modern European history. Could the Cold War and Poland being left to the Soviets after WW2 have been averted as a consequence of the Promethean principle? Probably, but we'll never know.
Would Anders have been released from HMG's servitude had Pilsudski exerted pressure on Churchill? Again, most likely. Sikorski was a great man but I think he was too "nice". Pilsudski, I think, had a better grasp of realpolitik - this is what was needed for a leader of Poland through WW2.
A Pole fighting for someone else evinces praise as being the 'gallant Pole'. When the Pole passes the cap around searching for some help in kind, the comment is usually 'that quarrelsome Pole' trying to undo the established order. Europe has never understood Poland, and whilst Poland has understood in part how Europe works, it has rarely grasped the correct manner to deal with Europe. Pilsudski understood the dynamic well, and, more importantly, knew just how to play the game. He was mostly a man of honour and chivalry, but also understood that honour and chivalry won't stop a German or Russian bullet, nor would it compel Poland's 'Allies' to stick to their word.
Of course, the above is pure speculation, but the possibilities could have been far different.
Piłsudski did not make peace with either the Reds nor the Whites because he wanted the Ukraine.
With respect, incorrect. Pilsudski did not join the Whites because, amongst other things, he foreshadowed Denikin's absolute intolerance to Polish Independence, not to mention Denikin's position that Ukrainian independence would have been tolerated even less. Pilsudski in part saw the resurgent Whites as more of a threat than the Bolsheviks too.
He decided to let them fight it out amongst themselves whilst building on Poland's strength for the coming showdown with the victor. Both were anathema to Poland, and Pilsudski had no obligation to help.
Realpolitik as practiced by Pilsudski.