Yes, Eastern Ukraine has a lot of Russian sympathizers who are descendants of the Russians who Stalin relocated there after he starved half the country to death.
They do want continued relations with Russia, especially economic, but are not crazy about Putin.
Above all they do not want war.
Western Ukraine is another animal altogether and if Putin tried to conquer Kiev it would be holy hell.
These folks can get very violent.
Link: https://www.youtube.com/watch?v=pbe9nhkxyC8