I don't think they can take and hold the whole country. However, if you say that even with our aid they are doomed, then I would consider that a black hole of money and material. I wouldn't drop anything more on them if it is hopeless either way. The Russians have already been bled at this point, they pose no real conventional threat to NATO. If it is hopeless for Ukraine to win, you are sacrificing them for next to nothing now. The equipment we are sending them is far more advanced than the Russian junk it is being used to blow up and that isn't even discussing the people being fed to the grinder.I don't think Ukraine can take back what they lost. Ukraine has the Napoleon and Hitler problem, there are a many more Russians than Ukrainians. Defense produces better kill ratios, along with some well timed counter strikes.
I am not sure Putin cares about losses, and so far we see no evidence the Russian people do. If no one cares if they lose 500,000 more, why would he stop.
Even with our aid I am not sure Ukraine can hold out. Without aid, it will be faster and much less of Russia's military destroyed.
Russia cracked the guerilla warfare nut in Chechnya. I am not sure we won't see massive Ukrainian deaths when it falls. Numbers to rival WW2 conquests.
I think they have a chance to hold the lines where they are if they remain on defense. I don't think they can mount an effective enough offense to change the current front lines much. So I think there is still value in making them a tough nut to crack. If they are doomed, it is kind of sadistic to ask them to keep killing themselves to blow up Russian junk that really poses no threat to NATO.