The 300 f/2.8 without a teleconverter should be tack sharp on the D800. There are reasonable limits as to how much you should crop, but the lens should be sharp.
With the teleconverter, you are trading off slightly on sharpness plus you are losing light. I'll assume shutter speed needs to be 1/1000 sec or faster for birds regardless of other settings. I willingly use the TC14E II and find the drop in quality minimal. I avoid using the TC17E II and TC20E III unless truly necessary as the softness and impact on aperture make a difference. When you use those teleconverters, you need to have excellent light and crop less than with a bare lens.
You need to be careful about expecting too much from severe crops on distant targets. I would avoid cropping teleconverter images beyond 50% unless you are comfortable with the drop in image quality.
If the subject is distant, the image is likely to be a little soft. Teleconverters just make it larger but still soft. It varies by lens, but I find beyond 100 yards most lenses are softer.