Yes, it is true, Harpo did smuggle papers out of the Soviet Union for the USA. You can read about it in "Harpo Speaks!"
I found this on the web for you at, http://www.users.muohio.edu/shermalw/honors_2001_fall/honors_papers_2000/lee_harpomarx.html
Harpo goes to Moscow
In the fall of 1933, Harpo received a call from his by then good friend, Alexander Woollcott: "I've decided that Harpo Marx should be the first American artist to perform in Moscow after the U.S. and the U.S.S.R. become friendly nations. Think of it!" (Marx, 1961, 297). Woollcott figured that with Harpo's pantomimic capabilities he would be a hit in Soviet Russia; Harpo decided to give it a try.
After a slight delay with the Soviet customs (they thought Harpo was a spy), Harpo was able to get into Moscow. He was assigned his own personal guide (spy to make sure he wasn't a spy) and given an appointment with the head of the department of Soviet theater to set up some dates for appearances; he wasn't given any. After a week of trying Harpo was ready to leave the country when the Soviet Foreign Minister (Stalin's right hand man, Litinov) rectified things and got him a Soviet group of actors to put together a show. For the show Harpo would play a harp solo, a sketch with his clarinet and a pantomime piece with the rest of the group.
Harpo's opening night in Moscow was arguably the best opening night in comedic history. "I'll be a son of a ***** if I didn't knock them out of their seats. . . . I only had to wiggle an eyebrow to bring the house down." (Marx, 1961, 317). The Soviet crowd was awestruck. At the end of the show Harpo would make curtain call after curtain call. On the next day, one Soviet critic would write that Harpo had received, "an unprecedented standing ovation, lasting ten minutes." (Marx, 1961,318). Harpo loved every minute of it, "No other success ever gave me quite the same satisfaction. Besides, it happened on my fortieth birthday." (Marx, 1961, 318).
In the six weeks that the show ran in Russia Harpo became a celebrity. The show was an incredible success. Everywhere it played it received the same enthusiastic response it had met in Moscow. Harpo had shown that comedy, particularly his, could transcend culture. It was the defining moment in his career.