Yes you can do such a disk but in my case with so close and 120° angle led, the closest led are polluted and you loose visual precision.
I tried it too lol.
I've got a CNC so I haven't got limit. There's PMMA in the ring holes too, this holes have a kind of tear shape, the bit I used is 0.8mm diameter.
Ring and screen window are one piece PMMA.
Make a full ring is difficult in my case, because of the circuit, there's bus inside the ring and i need to connect it, this is the way on my PCB.
And it was a very very very long work to route this part.