No, NIMA has more in common with Canada's Medicare than it does with government-run systems like the UK's National Health Service. As in Canada, care is financed through a government insurance system, but provided through the private sector, in addition to nonprofit hospitals and clinics.
Americans are already living under a socialized healthcare system. In our case, insurance industry profits are socialized through tax subsidies and high copays, while care is privatized. "Socialized medicine" is also an inaccurate description of most universal healthcare systems where businesses are not paying an average of $15,000 a year to contribute their share of the costs of an employee plan covering a family of four. Employer-provided insurance makes the costs of doing business prohibitive in many industries, while overseas competitors in many countries hold a competitive advantage.