You know it actually might be. Three big things it requires are Multi-Draw Indirect (looks to be available in 4.3), shader storage buffers (looks like it's also available in 4.3) and compute shaders which 4.3 should have too.
I don't know much about WebGL2 - do you happen to know if dropping the requirement to GL 4.3 would be enough to make it compatible with WebGL2?