Impossible pH For Aqueous Weak Acid Solution An aqueous solution of $\ce{HCl}$ has a $\mathrm{pH}$ of $0.00$ if $[\ce{H+}] = 1.00 \; \mathrm{M}$. I tried to see if an aqueous solution of acetic acid could have a $\mathrm{pH}$ of $0.00$, given that its $K_a$ value is $1.8 \times 10^{-5}$. I tried finding the concentration $[\ce{H+}]$ of such a solution using

$$K_\mathrm{a} = \frac{[\ce{H+}][\ce{C2H3O2^-}]}{[\ce{HC2H3O2}]}$$

and then using molar mass and density conversions to determine whether such an aqueous solution exists. 

Does it make sense to say that such a solution does not exist if the amount of substance of acetic acid in 1 liter of solution actually take up more than 1 liter of volume?
Your reasoning is fine. But a major caveat (or additional factor) is that the pH scale itself no longer applies to concentrated solutions (say, more than 1 molar in acid) where the molarity of water falls significantly below 55M (pure water). 

You can extend the pH scale down below 0 by empirically measuring how effective an acid solution is at protonating a weak base, but the scale deviates from the straight line predicted by the concentration of acid present.