No. There's no substitute for rigidity in fixturing and of the machine itself. There will also be vibration motions that have unpredictable nodes, frequencies, and amplitudes.
Consider that a 2 flute mill at 20,000 rpm will induce vibrations with a fundamental frequency of about 670 hz. This would require a servo system with a bandwidth of about 2 khz to correct, a sampling rate of 8khz would be a bare minimum.
Next, what to do if the tool digs in, and shoves the part? You have to have backlash sufficiently damped, and rigidity enough to keep the tool or part from being snapped off.
There's a good reason machine tools are as heavy and rigid as they are, and why they must be on a thick foundation, and leveled precisely before use.
If you're going high precision, you'll also have everything in a temperature controlled environment, and allow the materials to soak at a day to achieve the proper temperature. Cooling is very important when you get into fractions of a millimeter, or "tenths" (1/10,000 inch) tolerances.
The best machine tools are old American cast iron machines from about 1940 to 1960, rebuilt with modern control systems.
The only issue I have with this design is that the accuracy decreases with the distance from the rotary axis, hence it is not uniform over the building volume.
3d printers don't have forces pushing back on the print head, nor the vibration from a cutting tool to deal with.
This design might work ok for 3d printing, or laser cutting, or anything else where no contact between the working head and the material occurs.
As far as accuracy and repeatability, it's going to be about as good as the average 3d printer design. It's a nifty idea for a system, but it's only a decent machine for cutting if it's scaled up massively and built of cast iron or similar materials.
Optical tracking might be easier.
I'm not sure how much deflection you could actually tolerate before deforming the joints in the arm. Even with deflection tracking you might end up taking very, very shallow cuts. A 3D printer that runs for 16 hours in your apartment is annoying, a CNC mill running for 16 hours will be genuinely intolerable.
Yeah both humans and multiaxis cnc machines can articulate their arm to apply a tool to a work piece and both a sparrow and an F16 can fly through the air.
A sparrow can take off and land on a branch, and it regularly weaves through thick foliage no wider than its wingspan. So, I assume the human is the sparrow?