If Pelosi sits on the article forever, which she has strongly indicated she will, then the impeachment process is incomplete and is never certified. The House does not supercede the Senate or the Constitution. Pelosi cannot simply make up her own Law as she thinks it should be. If the impeachment is never completed and certified, it becomes more of a "censure" motion instead of a formal impeachment. That is, according to the House Trump was found meeting the standard of impeachment, but was never actually impeached. That is censure.
On the other hand, McConnell could hold a trial without the documents and simply dismiss the whole issue outright. He could hold a trial and then declare a mistrial. This would mean that Trump is exonerated.
I do not see a way that Pelosi can win this war with the Senate. McConnell is never going to give her control of a Senate trial that she is trying to extort. If she continues to flout the rules of proper procedure, McConnell can simply call 'foul' and dismiss the whole thing.