Modified from an earlier answer of mine

The video "Hired Thugs for the Rich" is complete nonsense despite its stentorian British narrator. Truth be told, I got only halfway through the video before I turned it off. The video is filled with half-truths, distortions (American firms continued to operate when the Nazis entered Paris- well, of course! The US was still a neutral in 1940!), and outright inaccuracies (contending that the chemical concern IG Farben made panzers, for example).

The relationship of industrial capital and the Third Reich is one that is highly complex and the nature of international business adds a further layer of complexity. In 1920s, American companies saw Germany as a plum market by virtue of its large population and high degree of industrialization. This led to large-scale investment in German industries and subsidiaries opened up. Opel, for example, was established with the help of GM as a parent company in 1928. These international relationships continued after the advent of Hitler in 1933, but were often freighted with new political meaning.

Hitler's drive for rearmament caused some alarm among German industrial circles. Although support for the Weimar Republic was very shallow among these types, they were seldom fans of the new order. Many German industrialists resented state interference in the running of the factory floor and while more than a few welcomed the Third Reich's anti-labor laws, they also became packaged together with NSDAP organs like the Deutsche Arbeitsfront which was a sinecure for NSDAP cronies. On the extreme end of opposition, Hugo Junkers, head of one of the most prominent aviation companies of the interwar period and a firm believer in the peaceful use of airpower, was put under house arrest and the state forced him to surrender his patents and shares in the Junkers firm. Most German industrial leaders sought a cooperative relationship with the Nazi state, but the example of Junkers was a chilling one for those that thought of resistance. It made a degree of business sense for managers to patronize the new order rather than resist it. Wilhelm von Opel, the chairman of Opel, spent lavish amounts on gifts to NSDAP elites and became the chief sponsor of the National Socialist Motor League. American-owned companies or their subsidiaries often had to deal with this new reality, but it was still an incredibly complex picture. The Third Reich encouraged the cartelization of the German economy, which already was one of the most centralized in Europe prior to 1933, and American multinationals had to operate in this environment. Opel, for example, had to comply with the 1936 Schell Program, which streamlined German automobile production making it more suitable for military use, but Ford's Cologne plant was exempt from these restrictions. In contrast to Ford, IBM lost day-to-day control of its German Dehomag, but the New York company also wanted to keep control of its near monopoly on tabulating machines, so it kept Dehomag in operation to preserve the company's monopoly in Germany.

IBM's case was paralleled in other major foreign-owned firms by the dawn of the war. While there were on paper owned by foreign concerns, they had been pretty much de facto German companies by this point. The management had been Germanized and Jews thrown out of positions of authority. The laws of the Reich prevented profits from cycling out of the country, creating a headache for accountants. Reports on day to day operations grew more distant and only more so after the war broke out. Foreign firms were complicit in this process of Germanization, some gambling that playing with the state would lead to a more normalized business relationship when the political atmosphere was more relaxed. Other responses were predicated on the fear that if they resisted, then the Third Reich would engage in outright expropriation and control. This was what lay behind the convoluted case of tetraethyl lead gasoline. This was an old technology from the 1920s whose American-owned patents and manufacturing data were relatively open. Italy had already in 1935 overrode these patents on its own accord and allowed a state-owned company to produce it. The fear in American circles (the US patent was owned by the Ethyl Gasoline Corporation which in turn was under joint control of GM and Standard Oil) was that Germany would follow the Italian precedent. Thus the Americans were more receptive to IG Farben's offer to form Ethyl GmbH with IG Farben, the German Standard Oil subsidiary, and Opel sharing ownership. The protection of a large patron like IG Farben would allow the US firms to keep their trade secrets under some form of control, but the subsidiaries soon became passive partners as IG Farben assumed more control over Ethyl GmbH. Fears of losing control were also quite acute in the financial sector, both German and non-German owned, as they often operated under implicit threat that National Socialism saw such unproductive wealth as suspect and tainted by Judaism, which in turn made financial institutions more conducive towards freezing Jewish assets or other fiscal measures pushed by the state.

The idea that the Nazis were "thugs for the rich" is a charge that actually dates back to the 1930s and was a staple of both socialist and communist propaganda of this time and in the later case remained an orthodoxy through the Cold War. It has also been taken as a given by various anti-capitalist movements seeking to tar existing multinational concerns like Ford with the taint of the Third Reich. Such contentions generate more heat than light. Hitler may have held Ford and Fordism in high esteem, but so to did many other world leaders at this time, including the USSR of Stalin which practically enshrined Fordist/Taylorist industrial management as state doctrine. The reality was of course far more complicated and part of the problem of examining American multinationals and the Third Reich was that of the latter's twelve-year existence, Germany was at peace with the US for eight of these years. American firms, like their German counterparts, found themselves having to adjust to a state predicated both on military expansion and a subordination of industry to the needs of the state. Most industrial leaders accommodated these demands, and more than a few profited from them, but many were uneasy with them. Even in giant German conglomerates like Krupp or Rheinmetall-Borsig which grew tremendously under state military contracts, their management found that they were no longer masters of their own house.

Therein lies the damage that videos like the one linked to by the OP. Industrial collusion and corporate profits from the Third Reich is a serious issue and one that American companies like Ford and GM have been less than forthcoming about, as well as German firms. A lot of businesses operating in Germany recast themselves after the war as principled opponents of Nazism, but this was far from accurate, and sometimes was a self-serving lie. But a hyperbolic argument that is unsustainable (hired thugs) actually makes holding these firms accountable much harder to accomplish and makes it harder to distinguish serious scholarship about corporate responsibility from noise.

As for the larger question of could an economic embargo have hurt the Third Reich, this is an unanswerable question. Certainly Nazi persecution of Jews and the overall unsavory nature of the dictatorship hurt the "made in Germany" brand as well as inspiring boycotts. But such actions had little sway in middle of the Depression. Certainly foreign investment could have pulled their out, but plant would have remained and been nationalized in such a scenario. The Third Reich's general approach to international trade was hat it had to serve the interrelated goals of rearmament and autarky. Thus its trading policy often involved selling finished goods, often military weaponry, to weaker countries in exchange for natural resources. The US market did not really figure much in this calculation. More proactive measures by the American government and business working in tandem might have added more pressure, but the Nazi economy was already suffering the pains of self-inflicted wounds by the late-1930s as it had to play a complex shell game with its books to finance rearmament.

Sources

Nicosia, Francis R., and Jonathan Huener. Business and Industry in Nazi Germany. New York: Berghahn Books, 2004.

Tooze, J. Adam. The Wages of Destruction: The Making and Breaking of the Nazi Economy. New York: Viking, 2007.

Turner, Henry Ashby. General Motors and the Nazis: The Struggle for Control of Opel, Europe's Biggest Carmaker. New Haven: Yale University Press, 2005.

Wiesen, S. Jonathan. West German Industry and the Challenge of the Nazi Past, 1945-1955. Chapel Hill, NC: University of North Carolina Press, 2001.

_. Creating the Nazi Marketplace: Commerce and Consumption in the Third Reich. Cambridge: Cambridge University Press, 2011.