Aside from electric instruments like @Aaron mentioned, this is not unheard of but extremely rare. I have seen a few upright basses over the years in bass shops with a cutout in the upper bout like this or even more pronounced.
I even found a pic of a viola with a similar feature:
I have never seen this on an acoustic cello or violin but I would not be surprised if there are some out there.
My take (and personal experience) is string players are used to and even rely on where the body meets the neck for physical cues on where to find upper register notes. Because of this most players prefer a symmetrical instrument. Even electric string instruments usually have some type of abbreviated shoulder because string players are used to a transition from neck to body.
As for acoustical properties, I cannot say for sure but changing the shape and symmetry of an instrument will probably have at least a minimal effect on the sound.