Against Communists who were going to steal their money and take their power,yes.
No.
Poland was already seen as a lost cause by the British, and really the British would be much more comfortable with the Soviets (who they were sure would soon fall and be replaced by a nice normal Russia) occupying it rather than some "dangerous expansionist state". (Really, the British had a huge bee in their collective bonnet about Poland. It makes for great comedy reading today.) The French, while more pro-Polish, weren't going to act without British backing.
Whilst being War-weary was certainly a thing, we are talking Communist Russia attacking, conquering and moving through Poland. The avowed goal of the Soviets was to conquer Poland to allow access to Germany and turn them Red as well. This is a threat to the stability of Europe. This isn't Lloyd George attempting to keep WWI going by supporting Greek expansionism, nor is it localised border wars in the aftermath of Versailles.
My gut would be that Freikorps would be allowed to operate in large numbers in the East of Germany, maybe geographically limited, with even expansion of the Heer allowed. Once the Red menace is suppressed, disarmament would recommence and the Freikorps would be disbanded. After all, the WAllies used Freikorps in the Baltic (at least initially) against Communists instead of their own troops.
And does your gut realize how hated the Germans were after WW1?
The British government would want the German state to remain strong, as would the American government (not that it would act), the British people, French people and American people would likely see it as a bunch of barbarians fighting another bunch of barbarians or worse. There will be those who will relish the thought of evil Germany getting its just deserts under a Bolshevik bayonet and there will be those who will see the Russians bringers of civilization.
Not that the Bolshevik armies could reach this far - if Germany falls to the Reds, it will fall to German Reds. The Russian Reds don't have the resources or logistics to drive into Germany.
When the alternative is having all of Europe fall to communism, the public would be more than willing to engage in a campaign against the Soviets.
Ha. Ha.
The Western public hadn't been exposed to 70 years of anti-communist propaganda and 70 years of hearing news of communist atrocities.
They were, however, very familiar with the incompetence and atrocities of their own governments. They're not going to fight the Russians because their governments tell them to.
IMO:
For the Soviets to win requires a miracle - probably one that involves Stalin not being in this area and the Bolshevik army having more competent leadership. So it's possible, but it would leave the Soviets with no gas in the tank.
Also, to invade Germany would require a change of rail gauge, so their logistics are constrained by more than only distance.
Poland could be occupied, but the Polish territories won't be quiescent. The Soviets will need a fair sized garrison.
Czechoslovakia would welcome the Soviet occupation of Poland (the Czechs were very anti-Polish and very pro-Russian - though this may -
may - change as the stories of refugees from Poland spread). The Czechoslovaks may occupy some border areas - for example, they claimed all of Silesia and may take the opportunity to grab Polish Silesia.
I really don't see Germany being allowed to take back any land from Poland. As I mention above, the Germans were hated back then. If Germany goes east, my bet is the French and Belgians threaten to annex the Rhineland between them unless they pull back and disarm their illegal army.
As for Germany itself... Might the arrival of the Red Army on the border trigger a Communist uprising in Germany? Maybe. Though enough of the German Communists disapproved of the Bolsheviks that the Red Army being on the border may discourage their participation in any uprising. If there was a revolution, would it be a serious one? Again, I don't know, but I doubt it. The most dangerous German revolts were in 1918 and 1919, the Russians are arriving a bit late.
So it is possible for Germany to go Red, but IMO not likely. A failed revolution might have interesting effects if the Soviets support it (almost certain to happen, though I doubt Russian troops would cross the German border - only volunteers, supplies and weapons) so the Rapallo pact may be butterflied.
A successful German revolution, on the other hand, likely means that Germany loses the Rhineland to an Entente supported "white Germany". Further, we might see Red Germany join the Soviet Union (in which case Russian control of the Soviet state is very much undermined) or we could see Germany and Russia decide that they are better remaining as two separate states (IMO more likely). Either way, both Russia and Germany would need to trade together heavily due to the rest of the world isolating them. Likely this would work out to the economic advantage of both. Almost certainly "Red Germany" and "Red Russia" would have ideological arguments - this could have interesting implications for the evolution of communism around the world, instead of two ideologies of the far left (Communism and Socialism) there would be three (Communism, Socialism and "Germanunism") but the states supporting two of them would be co-dependent even as the argued vociferously.
I think DrakonFin is right about the Baltic states - they're more vulnerable, but the Soviets had made peace and are pretty close to being clapped out. I think Lenin will leave them for the future.
It might not be wrong to say that in some ways losing in Poland was actually a boon for the Soviet state, as it showed some of its limits, directed its efforts inwards and made it start boosting its domestic strength for future challenges from the outside world.
I'm not so sure. After Poland fell, I would tend to think that they would realize they were stretched to their limits anyway.
An attack on Danzig or Romania might be possible, I suppose. I would have thought that defeating the Whites in Russia itself would have had a higher priority to those however.
An attack on Danzig or Romania could get rather interesting, depending on the details.
fasquardon