Yes, they can continue to go pink and have an MM as long as they have market makers piggyback 15c2-11. But that somewhat depends on what their future plans are.
OTC Markets (Pink Sheets) is just a paid PR company with no regulatory authority. The "alternative reporting methods" is meaningless, and so many of the companies that do it are fraudulent. The disclosure is not accurate, and in many cases intentionally misleading to further pump and dumps and/or outright scams. You should not rely upon such disclosure.
But yes, the shares will keep trading but do not expect they company to continue to provide any disclosure to shareholders and, if they do provide something, do not assume it is accurate in the absence of any regulatory oversight. Which is why serious investors, including the vast majority of institutions, won't touch a non-SEC reporting pink sheet company.