Of course not, we can't even simulate how one protein folds.
Larger proteins (a few alpha helices and beta sheets), the folding process can be studied if you start with structures near the native state.
None of this means to say that we can routinely take any protein and fold it from unfolded state using simulations and expect any sort of accuracy for the final structure.
Other people use ab initio very differently (for example, since you said "level of theory" I think you mean basis set). I don't think something like QM levels of theory provide a great deal of value on top of classical (and at a significant computational cost), but I do like 6-31g* as a simple set.
Other people use ab initio very differently. For example, CASP, the protein structure prediction, uses ab initio very loosely to me: "some level of classicial force field, not using any explicit constraints derived from homology or fragment similarity" which typically involves a really simplified or parameterized function (ROSETTA).
Personally I don't think atomistic simulations of cells really provide a lot of extra value for the detail. I would isntead treat cell objects as centroids with mass and "agent properties" ("sticks to this other type of protein for ~1 microsecond"). A single ribosome is a single entity, even if in reality it's made up of 100 proteins and RNAs, and the cell membrane is modelled as a stretchy sheet enclosing an incompressible liquid.
I also agree that QM doesn't provide much for the cost at this scale, I just wish the term ab initio would be left to QM folks, as everything else is largely just the parameterization you mentioned.
I am more than happy to use "ab initio" purely for QM, but unfortunately the term is used widely in protein folding and structure prediction. I've talked exdtensively with David Baker and John Moulton to get them to stop, but they won't.
In inorganic materials ab initio means you actually solve Schrodinger's equation (though obviously with aggressive simplifications e.g. Hartree-Fock).
Having developed a few newtonian force fields, calling them "derived from QM" is very, very generous :P
I looked at the various approaches and sided with folding@home. At one point I had 1 million fast CPU cores running gromacs.
but, as I pointed out elsewhere, this would not be particularly helpful as it would use an enormous amount of resources to compute something we could probably approximate with a well-trained ML model.
It also wouldn't address questions like biochemistry, enzymatic reactions, and probably wouldn't be able to probe the energetics of interactions accurately enough to do drug discovery.
Now, the question is, does it matter? When do you EVER need to know the exact atomistic, yet alone electronic, trajectory of a single protein starting from a given position within a cell surrounded by waters in a given configuration?
It doesn't really matter. This is the beauty of noise and averages and -- dear to me-- statistical mechanics. At finite temperatures, AKA most everything we experience as living things, quantum details (or precise classical trajectories for that matter) aren't that important for the vast majority of questions we tend to have about a system.
Why am I saying this? Because I thought the same as you and it took me 20+ years to realize MD doesn't affect medicine at all.
This is the only real update of the year: https://foldingathome.org/2022/01/03/2021-in-review-and-happ...
SARS-CoV-2 has intricate mechanisms for initiating infection, immune evasion/suppression and replication that depend on the structure and dynamics of its constituent proteins. Many protein structures have been solved, but far less is known about their relevant conformational changes. To address this challenge, over a million citizen scientists banded together through the Folding@home distributed computing project to create the first exascale computer and simulate 0.1 seconds of the viral proteome. Our adaptive sampling simulations predict dramatic opening of the apo spike complex, far beyond that seen experimentally, explaining and predicting the existence of ‘cryptic’ epitopes. Different spike variants modulate the probabilities of open versus closed structures, balancing receptor binding and immune evasion. We also discover dramatic conformational changes across the proteome, which reveal over 50 ‘cryptic’ pockets that expand targeting options for the design of antivirals. All data and models are freely available online, providing a quantitative structural atlas.