Not really. With IE vs. Netscape, Microsoft tied IE into an existing monopoly (its Windows 95 OS). There is no smartphone monopoly or mobile advertising monopoly. Even if you consider Google's search and/or ad positions a monopoly, Google isn't giving Android away for free in association with its monopoly, it's giving Android away for free independent of its monopoly (as evidenced by Android phones that don't use Google services by default, instead using Baidu, Yahoo, etc.). IE was tied into the Windows 95 OS, so customers had little choice in using it. This doesn't even consider the various agreements Microsoft made with OEMs.
Also, behavior that is illegal or unethical for a company with a significant monopoly (e.g. Microsoft in the 1990s) may be legal or ethical for a non-monopoly company (e.g. Google's smartphone business in the 2010s).
Edit: I will add that Netscape's business model was probably unsustainable regardless of IE being free. Web browsers are better off being free.