Well, for gases that behave ideally there is a linear dependence between molar mass and density (for a given pressure and temperature), so you are right that comparing molar masses is equivalent to comparing densities.
You are also right that for any mixture of a gases there exist an equivalent molar mass, which is a weighted average of molar masses of all gases present.
But no, molar mass doesn't look like a density - density is per volume, not per mole.
If the acetone boils it produces a huge volume of gas, so it can fill up whatever volume is available, replacing the air.