I can offer an answer to the first half of your question.
The short answer is: no. The promotion of traditional Chinese medicine during Mao’s lifetime wasn’t intended to compensate for any brain-drain that occurred during the rise of the Chinese Communist Party (CCP). In fact, the CCP initially tried to build a modern medical system modelled on Russia, which merged or supplanted traditional Chinese medicine with Western medicine.
However, like so many things in China, healthcare became a political battleground, as the CCP fought to distance themselves from Russia and the West, in order to forge a uniquely Chinese brand of communism.
As Volker Scheid and Sean Hsiang-lin Lei explain in “The Institutionalization of Chinese Medicine” (Medical Transitions in Twentieth-Century China, eds. Bridie Andrews and Mary Brown Bullock, Indiana University Press, 2014), from about 1954 onwards the CCP began to turn against “biomedical physicians whose policies were guided by professional rather than ideological agendas and who resisted political control by the [CCP].” (p. 253). Essentially, because physicians weren’t prepared to blindly submit to centralized CCP policies, they were considered untrustworthy. As a consequence of this, the CCP began to heavily promote traditional Chinese medicine, which was seen as more politically aligned with Chinese communism. A modern parallel of this is what’s happening right now in the US, where the advice of the Centre for Disease Control doesn’t always align politically with the Trump administration and is causing tension between the two. Since the 1950s, traditional Chinese medicine has been part of China’s plural health care system (combining traditional medicine with Western medicine). In 1982, it was enshrined as such in the PRC’s constitution.
When you asked whether traditional Chinese medicine was harnessed to combat the results of brain-drain, you might be thinking about the barefoot doctors that Mao promoted during the Cultural Revolution. The barefoot doctors were health workers sent out into the countryside to serve the peasant population. Prior to this, most medical care was only available in urban centres. The barefoot doctors were meant to embody Chinese revolutionary zeal – striking out into the countryside with minimal training, but a strong desire to Serve the People. However, it’s important to remember that this was politically motivated, not a necessity driven by brain-drain. Also, as Xiaoping Fang explains, while “their main equipment was popularly described as ‘one silver needle and a bunch of herbs,’ a reference to acupuncture and Chinese herbal medicine …” the barefoot doctors “combined Chinese and Western medicine in medical practice.” (p. 268 “Barefoot Doctors and the Provision of Rural Health Care” in Medical Transitions in Twentieth-Century China).
I hope this answer makes sense. I’m sorry I can’t provide you with any information about the commoditization of traditional Chinese medicine in America. Good luck in your search for more info :)