I think Wallace was just deeply idealistic and probably a true Socialist at a time when Americans could not differentiate between Socialism and "evil" Soviet Communism (well...Americans still can't do that), and that his idealism allowed the Soviets to use him to their advantage. But I definitely don't believe he was a spy or even a conscious Soviet asset.
Calder Walton wrote a book last year called Spies: The Epic Intelligence War Between East and West (BOOK | KINDLE | AUDIO) that was published my Simon & Schuster and I actually posted this excerpt a few months ago about Wallace and the Soviets during the Cold War that might answer your question a bit better:
Russian archival records obtained for this book show that [Joseph] Stalin colluded with his favorited U.S. candidate in 1948, Henry Wallace, [Franklin D.] Roosevelt’s Soviet-friendly wartime Vice President.
The nature of Wallace’s relationship with the Kremlin has long been a subject of speculation. Soviet intelligence is known to have unimaginatively code-named the Vice President CAPTAIN’S DEPUTY during the war. But no evidence has ever emerged that Wallace was recruited as a Soviet agent. He was, however, we can now discern, a Soviet tool. He sincerely believed that “peaceful coexistence” between the Soviet Union and the United States not only could be achieved, but was essential for world peace. All the while, he looked away from (and naively followed Soviet propaganda denying) the existence of Stalin’s mass forced labor and terror programs. According to [President Harry S.] Truman’s counsel Clark Clifford: “It was never clear to me how aware he [Wallace] was of the uses to which the Communist Party was putting him, but whether he knew it or not, he was following the communist line, serving communist ends, and betraying those Americans who supported him as a serious alternative to the two main candidates [in 1948].” Wallace’s naivete about Soviet communism turned him into an asset for Stalin, if not a recruited Soviet agent.
Wallace decided to run in the 1948 U.S. election as the Progressive Party nominee. In April and May that year, he secretly liaised with Stalin about public policies that would be advantageous for the Soviet Union, coordinating his public statements with the dictator. Wallace secretly met with the youthful Soviet ambassador to the UN in New York, Andrei Gromyko, who dispatched the candidate’s messages to the Soviet foreign minister, [Vyacheslav] Molotov, and to Stalin himself. In his memoirs, Gromyko admitted to meeting Wallace, but downplayed the meeting’s significance, suggesting that after talking with him he considered that Wallace had lost contact with the pulse of American life. Archival documents in Moscow reveal that in fact Stalin took Wallace’s position and candidacy seriously, approving his public positions, and answering questions that the former Vice President put to him, which Stalin annotated in his distinctive pencil. Their alignment produced a published open letter from Wallace to Stalin, vetted by the Soviet leader in advance, to which Stalin then publicly replied, all as agreed between the two men.
Wallace’s Presidential election bid in November 1948 dismally failed; he ended up getting barely 2 percent of the vote, while Truman, to his and the nation’s surprise, won a second term. He defeated New York Governor Thomas E. Dewey in one of the greatest upsets in U.S. Presidential history. Ironically, the staff of Wallace’s failed 1948 campaign included none other than the Soviet atom spy Ted Hall. Following his unsuccessful White House run, Wallace had a crisis of faith in his pro-Stalinism. This may have been caused by his realization that Stalin had used and discarded him after the election. Stalin had gotten what he wanted from Wallace. In 1952, Wallace published an article, “Where I Was Wrong,” describing “Russian Communism” as “utterly evil.” The Kremlin and its intelligence services nevertheless learned an important strategic lesson for later in the Cold War: that it could use the freedoms inherent within American electoral campaigns to influence candidates favorable to the Soviet Union.