No, FDR did not campaign to the right of Hoover in 1932. He campaigned very much to the left of him. However, the Democrats did call Hoover a "Socialist" during the 1932 campaign, but not for the reasons you assume. The attack was political payback for what had happened four years earlier.

In 1928, Herbert Hoover ran against Democratic candidate Al Smith and won in a landslide. Late in the campaign, Hoover characterized Smith's policies as supporting "state socialism". Smith refuted the attack, while Republicans rallied to Hoover's side.

An October 27, 1928, AP article explained:

"A further definition of 'state Socialism,' the term used by Herbert Hoover in his New York speech to characterize certain policies of Governor Smith, was on the books today following the speech here last night by Charles Evans Hughes, forrmer secretary of state.

"What Mr. Hoover meant by 'state Socialism', said Hughes, 'is plain. He used the term in its proper sense as applied to the Bismarckian philosophy of the centralization of government dominating all the activities of the people. Mr. Hoover is a liberal and is opposed to state Socialism.'"

So, four years later, now that the stock market had crashed and the Great Depression was in full swing, the Democrats hit back at Hoover, using his own attack against him.

On October 5, 1932, former Missouri senator James Reed made a speech denouncing Hoover in no uncertain terms. Another AP article:

"Former Senator James A. Reed of Missouri, in his recent speech at Claremore, Okla., assailed the Hoover policy of doling out billions of dollars of taxpayers' money to favored banking and railroad corporations, terming such practices 'capitalistic Socialism.'

"On this subject, Senator Reed said, in part: "'I call attention to the fact that Republican leaders attack Roosevelt for declaring that present conditions should not be permitted to exist. They go so far as to charge him with being tainted with Socialism.

"'I affirm that Hoover has established Socialism in the United States.

"But it is not the Socialism of the proletariat. It is capitalistic Socialism, inaugurated not for the benefit of the common man or the small merchant, but for the benefit of the great banks and trust companies which have been overloaded with rotten paper.

"'Out of the taxpayers' money and out of the credit of the country, it is proposed to advance billions of dollars to these institutions. What is that but capitalistic Socialism?'..."

FDR's running mate, John Nance Garner, made similar attacks during the campaign against Hoover and the Republicans.

The Democrats certainly did label the Republicans "capitalistic Socialists" in the same way someone later on might use the term "corporate welfare". Nevertheless, FDR and the Democrats ran well to the left of Hoover and the Republicans in 1932.