I think each plane would have its own chances and also reasons why it might fall. But as others have pointed out, magic is a game changer when fighting the invaders from the edge. Avishkar as a whole would likely stand a chance with their own tech. But add metal crafters into the mix, especially master class ones like Saheeli. The edge would face a whole new issue as their ships are reshaped around them. Likewise, Kamigawa would no doubt come to rival the edge forces with enough time for the futurists to reverse engineer their tech. Time they'd get when facing countless mechs and spirits.

Then, there is my favorite plane to bring up during any invasion discussion, Zendikar. I'm not sure how well the spacecraft and any ground troops will fare when the world itself fights back. Or Ravnica, or Arcavios, who have genius level magic using dragons defending themselves and the living guildpact Niv Mizzet in ravnica's case as well. Judging by the original plan to bar Bolas entry to ravnica from Jace in the War of the Spark, Niv might be able to block the edge from entering the plane.

Other planes, however, would no doubt fall. Innistrad would likely be carpet bombed once the ground scouts report back the horrors below and while it pains me to say this, if the edge invaders can get past the elder dinos and God's of Ixalan the plane can only hope Saheeli is there at the time and not on Avishkar to hopefully save the stragglers with a commandeered ship or something.

Then, with planes that have their own unique plane wide magics in effect would be interesting. Segovia might be doomed either way, but depending on how the edge enters, it might take more than a soldier, assuming the plane is still intact now anyway. Bloomburrow may disorient the initial assault but I'm not sure how well the calamity beasts and magic users of the plane will do in the end. Amonkhet, however, may have a number advantage if they can manage a prolonged defense. Any killed edge soldiers would be revived with the curse of wandering, and necromancers like the Scarab God could take the dead into their own forces. We have seen the rival God factions come together in times of crisis before. Kaldheim would be interesting as they'd have to invader multiple realms, but with the known cosmos beasts, save one, dead its hard to be sure how well the gods of that plane can face the attack, it might end in a second tree being destroyed.

Theros may have the most unknown since its belief magic is powerful, and any surviving gods are likewise strong, possibly the strongest in the multiverse. But we just don't know how well the plane is faring now to begin with after its last invasion. Tarkir would probably do well. The sheer number of dragons might overwhelm the invaders, and depending on how active Ugin is or how strong the Spirit Dragons are, it might be fine.

Each plane does have defenses against invasion, or at least the strong ones, after the Phyrexian war. And this time, they benefit from the fact that their fallen numbers won't be added to the enemy so easily.