I’m no expert on Hungarian history, but it seems this topic might be interesting:
1. Did Hungarian Soviet Republic, the one established in 1919, have a potential to last longer than four months?
2. WI Kun decides not to trust the French/Romanians and doesn’t withdraw his troops from Slovakia? Is there even a remote possibility that Hungary might end up with Slovakia annexed or made into a puppet state?
3. Or alternatively WI Romanians do pull back their troops, possibly averting the Hungarian-Romanian War of 1919?
4. Supposing Hungarian Soviet Republic survives for at least few years, how does that change the situation in central Europe?
1. Define potential. Could it survive on its resources alone, against all the problems facing it? Almost certainly not. Could it survive in the context of a more broadly successful revolutionary wave? Its chances certainly improve.
2. The military balance of power between the Czechs and the Hungarians was roughly equal, and if the Hungarians had decided to stay the Czechs probably couldn't have forced them out on their own. So this question depends on the international context. The Romanians don't really mind Hungarian troops being tied up in the north; such a situation gives them the opportunity to move to the Tisza and claim it as a reasonable international boundary, while the Hungarians can't really do much about it. However, they have no interest in occupying more of Hungary, and not even necessarily in regime change. Any Hungarian government in these circumstances is going to be revanchist. The French, on the other hand, are going to be incredibly pissed, first that Kun is weakening their proxy Czechs, and that he's snubbed them. So again, it all depends on how much support Kun is getting from outside Hungary, in the form of other workers' states or even abortive but troublesome risings in strategic spots.
3. Having a Slovak Soviet Republic and a Red Hungarian border east of OTL is moving into wank territory. It's true that the Romanians don't want to rule a bunch of restive Hungarians, but they also want a natural boundary, and were historically taking any chance they could get to claim the Tizsa. The reason they did not get it is because of Allied pressure, even after capturing Budapest. So there'd have to be some REALLY compelling reason for the Romanians to do this, and I don't see one, unless the Russians are vastly more successful in Bessarabia. Nothing the Hungarians do is going to avert the Romanian-Hungarian War.
4. Geopolitically, it probably doesn't. Hungary in the OTL interbellum was a revanchist problem child who nobody really liked. Hungary in TTL's interbellum will be a communist revanchist problem child who nobody's really going to like. The only thing that would change would probably be its sponsor; instead of Germany or Italy, Hungary will be looking to the USSR (assuming it exists, and assuming there isn't a Red Germany or Red Italy, in which case it will have more than one sponsor). Politically, it probably doesn't either...much. The OTL interbellum governments in Romania, Austria, and Yugoslavia were anti-communist and authoritarian; ITTL you'll probably add Czechoslovakia to that list.
Then again, I like my butterflies small, so I'm prejudiced.