No, it will never be 100% accurate. Air or water are quite well described by the Navier-Stokes equations assuming the fluid is a continuum. Usually it is also assumed that they are Newtonian fluid.
The Navier-Stokes equations for a turbulent flow must be solved numerically (for some laminar flows analytical solutions exist). Numerical solutions are never exact for these problems, no matter what kind of order of accuracy you use for your discretizations (FDM, FVM, DG, FEM,...). There will always be some numerical errors (I am now ignoring turbulence modelling, because it is obvious that the closures are always only approximate, the only hope for exact stuff would be in DNS).
Even if you solve the Navier-Stokes solutions exactly (as you can do in some laminar flows), you only solved the model equations. Real fluids are made of molecules, not a continuum. You could do molecular dynamics solution (see https://mattermodeling.stackexchange.com/questions/tagged/molecular-dynamics) but you will again solve some model equations - with some potentials between molecules and atoms. Real molecules are made of nuclei and electrons. The electrons interact in a difficult way and quantum effects will appear. There is inherent randomness in them. Again, models for many particle quantum systems exist - like DFT or H-T, but there are approximations inherent in their formulation.
Less importantly, nuclei are obviously also compounds of nucleons, which are interacting by some complicated potentials through pions, but more exactly actually again made of quarks).
Each of the steps of course require immense computational power even for some small problems, but there are barriers of other kinds in the models themselves that made some aspects essentially random.
And then the whole issues of unknown initial conditions, unknown boundary conditions and deterministic chaos. Those are very important for actual solutions for a given time, less important for time-averaged values.