The short answer is "not really, unless you count leaving the gold standard as part of the New Deal."

The longer answer is that the New Deal is not a single program, but an "alphabet soup" of different things, including the creation of dozens of new organisations and pieces of legislation, each with its own acronym. Price Fishback, summarizing an enormous body of research, writes: "Seeking a pithy statement about the New Deal, people commonly ask: Was the New Deal a Success? The answer depends on a variety of factors: what policies are included, which outcomes are being measured, how large must the effect be to be considered a success. It is a treacherous effort to try to define a unified theme for the New Deal because there were so many objectives, often conflicting, that were being addressed." Each reform had some effect on some aspects of the economy. Some of them probably helped a bit, others probably impeded recovery. Most just shuffled resources from one pile into another without having much macroeconomic effect, helping some people and harming others, or boosting some social outcomes (crime, mortality, etc) without necessarily having a big economic effect. This scattergun experimentation was intentional; FDR was a policy pragmatist who gave almost anything that might work a shot, rather than a perfectionist with a predetermined set of coherent policies.

Paradoxically, the New Deal was also quite small in terms of its net fiscal impact. FDR was willing to pass quite radical legislation changing the economic laws of the land, but he was much more reluctant to run large sustained budget deficits. If you want to change a country in the long term, changing the underlying laws about employment, taxation, investment and so on is a great way to do it. Many of the reforms introduced would endure at least until Ronald Reagan. The Banking Act of 1933 fundamentally changed American finance; the Wagner Act almost completely transformed industrial labour relations not only in the US, but also in Canada and Japan where US legislation was copied; Social Security remains one of the largest and most popular government programs right until the end of the 20th century.

But if you want to stimulate employment and investment in the short run, what you need is government spending in excess of taxation, and that largely didn't happen. The line usually used, at least by center-left economic historians (Romer, Krugman, DeLong, Eichengreen, etc...) is that fiscal stimulus wasn't even tried in the great depression; it probably would have worked, but we can't know for sure.

Monetary stimulus was much more powerful. The previous monetary regime, the international gold standard, tied the hands of central banks, and the Fed was no exception. So long as the link between money and gold had to be maintained domestically (that is, holders of USD can exchange their currency for gold and vice versa), the central bank had to effectively accept inflation or deflation based on gold flows and demand for currency. Monetary reflation of the kind practised by post-1973 central banks in times of crisis would almost instantly force the US off the gold standard. FDR, unlike Hoover, was willing to accept this as a necessary consequence of saving the banking system.

Leaving gold worked - the US went off the gold standard in 1933, causing large unsterilized gold flows into the US, and reflating the economy. The ongoing banking crisis stopped, deflation ended, and aggregate demand recovered throughout the 1930s. The case for this was made most strongly in Christina Romer's landmark 1992 paper "What Ended the Great Depression?" but this is now the orthodox interpretation, and is consistent with the experiences of other countries: staying on gold was a heavy burden, and recovery generally begins after exiting the gold standard.

The case that the New Deal actively impeded recovery is tricky to make, because of the complicated and interlocking set of interventions, all in the context of a broad and fairly rapid recovery from an extraordinary cataclysm. Mostly, one must believe that government intervention is fundamentally inefficient, and that markets recover quickly by themselves, which is more of an underlying ideological belief than something that can be shown clearly in the historical evidence. Nobody I know would describe Price Fishback as a raging leftist, but his analysis nevertheless tends to show small and mixed effects, not a heavy boot of government intervention stifling recovery.

(Nitpick: The "return to normalcy" was Warren Harding in the 1920s, not FDR in the 1930s.)