No, I think Ukrainian battlefield success is by no means completely dependent on Western military equipment. The Ukrainian Army is becoming more regular and professional as the russian army becomes more irregular and amateurish.
Certainly, on the Kharkiv (now Luhansk) front, Ukrainian mechanised units are just eating their russian counterparts for breakfast in any meeting engagement.
The whole russian "army" has become a fragmented mess of regulars (very few with the stomach for more than operating artillery), collaborationst militias, chechens, wagner mercenaries/convicts and other dregs. While the best Ukrainian formations have improved their capability in impressive fashion since the summer, the russians have deteriorated even more.
The russians may once have understood how to perform high-tempo operational level manoeuvre war, but they certainly don't understand it now.
Western weapons have been, and are, crucially important to Ukraine. But, unlike some recent recipients of Western aid, the Ukrainians have shown the will, determination and skill to use this aid to decisive effect.