Well, there was the famous effort by the Poles to put a pretender on the Russian throne; but I suspect that, even if it had succeeded, you wouldn't have seen the Poles totally fold Russia into their own domain.
So, lets go a slightly different track: Lets say that the kibosh gets put on Muscovy. There was a good deal of conflict between the Grand Duchy of Lithuania and Muscovy and several invasions of the later by the former. Lets say that Lithuania gets lucky, totally destroys the Muscovy army and burns the city. Muscovy does into decline and never really recovers.
Now, when the Khanate crumbles, rather than having a strong Moscow to move into the power vacuum, you've got nothing; Russia becomes a hodgepodge of warring duchies and city-states. Novgorod is probably the strongest and might be able to form some kind of hegemony over the northern Russian states, but doesn't move into the interior.
Now, we've probably butterflied away a union of the Polish and Lithuanian crowns here (although I suppose Lithuania would be even more likely to convert and seek an alliance with Poland, since it can't play Poland and Russia off of each other, and still has the Teutonic Order to worry about). So that goes either way: either you still have a merging of Poland and Lithuania, or possibly Poland seeks permission from the Pope and launches a northern crusade against the Lithuanians. Either way, Poland comes into that territory.
With nothing to the east but fragmented duchies, Poland would probably seem to move into these Russian lands, especially those along the Baltic and its river ways.
So I think that Poland would ever move past the Urals (or even get that far?) Probably not; I doubt it has the population to really do so. But I think it might be able to gain control of modern day Ukraine, Belarus, and much of European northern Russia.
How strong would its control over the population be? Hard to say. The religious differences are going to be sever, plus just the general size of the realm. However, I could see the nobility becoming Polonized as the Lithuanian (and parts of the Ukrainian) nobility were in OTL.
Any thoughts?