No, he did not. He was respected by Stalin and most other Communist party officials, but he was always a rubber stamp. There is not a single documented case of him opposing something Stalin did, or attempting to act against Stalin or even before Stalin. Kalinin was loyal and just played along, knowing that he could keep his top job. He was known affectionately to Soviet citizens as Kalinych.

However, Kalinin was also kept under Stalin's power. He was constantly "guarded for his safety" by NKVD guards, who really kept him under Stalin's control. His own wife was arrested and remained in prison and tortured from 1938 to 1945, and was released only slightly before his death. Many friends were executed too, but he remained loyal to Stalin.

So no, Kalinin was a submissive rubberstamp.