It would help if the Soviets weren't adventuring in Finland at the same time, and removing the Purges would help even more. But...
I could see them trying it. Stalin really didn't seem to understand the abysmal shape of the Red Army, and it was at least big- 2 million men under arms, with a mobilization to 11 million being pretty straightforward. And quantity has a quality all it's own, and all that. Hell, as it is they used seven armies to invade Poland. Add the four armies used to attack Finland and they might think that they had overwhelming odds in their favor. OTOH they also did clearly seem to think that they needed more time to whip the Red Army into shape before confronting Germany. They were paying them off for a reason, after all. I guess I'd put it in the category of "I wouldn't be surprised, but I think it's very unlikely."
How would it go? Less certain. Surprise helps, and since the Germans were expecting an invasion from the east anyway surprise is probably possible. How suspicious were the Germans of just such a move at the time? I would think they'd have to have been idiots not to bear the possibility in mind, and they clearly weren't idiots. The Soviets didn't have the T-34 yet (panzers have been proven to eat T-26s and BT tanks for breakfast) and their operational skills had yet to be honed over four years of warfare.
I'm inclined to think that it goes poorly for Mother Russia.
The Allied reaction depends upon how the Soviets spin it. Especially if they send clandestine word of their intentions to "protect Poland" ahead of time, the reaction might be very favorable. At least until the Allies realize that the Polish government was being liquidated in favor of a communist replacement. After that, a three-way war! Woot! Until then, though, if the Germans start moving troops eastward at some point maybe the Allies take the opportunity to heat up the Phoney War.