This depends on which Macross that Frontier is based off. If it's based off the movie, yeah just about everybody on Earth is dead. If it's based more on the TV series, only about 70% of the Earth's population was destroyed by the Zentradi final attack.
Thing is, if it is based only on the movie, the 50,000-70,000 human survivors on the SDF-1 Macross couldn't possibly have procreated to the degree necessary to launch SEVERAL Macross-style colonization fleets AND colonize other worlds like Eden within the 50 year period between the end of the war and the start of Frontier. Even if you took the Zentradi population joining the human race into account, it's just not biologically possible.
I'm assuming that what we've been seeing since the first Macross TV series and the DYRL movie is some hybridized universe that allows for more humans to have survived the war. The TV series' population count, the DYRL's incidents, mecha designs, etc.