No, not necessarily. That is of course their ultimate objective - but how realistic it is in the face of Realpolitik remains to be seen. Perhaps sadly those regions are lost permanently. But for any nation invaded by another, preserving their capital, their government, their culture, their freedom and their borders at the time of that invasion is surely the first priority. Given they were expected by Putin - and not a small percentage of the same isolationist voices constantly predicting their imminent doom each week - to have folded like a pack of cards MORE THAN A YEAR AGO, where are we now? The Ukrainians have taken back a significant amount of territory despite all the apparent (but clearly inflated and inaccurate) odds.
Whatever issues of supply, munitions and equipment faced by the Ukrainians, and whatever the ebb and flow of the front line, the Russians clearly face exactly the same problems, and face them magnified by a greater factor. So the net result is neutral at worst.
And that's without accounting for the significant disparity between a motivated army of people fighting for all of the things listed above, and one of poorly trained, poorly equipped and increasingly conscripted men fighting for a cause which must look increasingly pointless and hopeless. That the Russians best troops are a blend of mercenaries and indentured convicts should send a huge message..