Yes, this is correct, which is why we can say it is definitively ruled out by current observations. We don't need to bother to modify anything to examine the Milne model: we merely compare our parameter estimates and see if the "total density = 0" case is ruled out. And it is to around 100 standard deviations with a combination of baryon acoustic oscillation and WMAP data (with this combination of data, [itex]\Omega = 1[/itex] to within about a percent at one standard deviation).
You can attempt to get around this by proposing that the CMB doesn't come from the phase transition in the early universe from a plasma to a gas, but then this presents two problems:
1. Why is the frequency spectrum of the CMB nearly a perfect black body? A large collection of distant stars, for instance, will not produce a black body spectrum.
2. Why is the baryon acoustic oscillation effect visible at all? This effect is a correlation of an angular scale on the CMB with the typical separation between galaxies in the nearby universe. It isn't a trivial correlation, but instead a correlation that relies upon the physics that would have been active when our universe was still a plasma.
If you want to get around saying that there was an early hot plasma state, you need to present a new model that predicts both of these effects (as well as others, such as the primordial helium abundance). If you don't, then the Milne cosmology is ruled out to hundreds of standard deviations, not even counting the obvious fact that there is matter in the universe, while the Milne cosmology assumes none.