Successor - Yes

To show that David was humble and not after power, after Joseph died, he could have asserted his right to lead but did not:

I will tell you that he (Joseph) had so much confidence in me that in July, 1834, he ordained me his successor as "Prophet Seer and Revelator" to the Church. He did this of his own free will and not at any solicitation whatsoever on my part. I did not know what he was going to do until he laid his hands upon me and ordained me.

Now, bear in mind brethren, that I am not claiming this office; as I have told you, I do not believe in any such office in the church. I was then in error in believing that there was such an office in the Church of Christ. (David Whitmer, An Address to all Believers in Christ, p. 55; "The Successor of Joseph, the Seer," Ensign of Liberty 1 (December 1847): 43-44)