[Eridrus]

I think it should still be possible, but it will depend a lot on the length of the holes too.

If you imagine a really long tube, any light entering at an angle will eventually hit the side, and if the sides do not reflect any light, nothing will come through the tube.

I don't want to bother doing the math to figure out how big the diameter of the sundial would have to be to have sub-minute accuracy, but I think it is very possible.

[jerf]

skykooler's point is that the Sun is not a point source. I think you may be mentally modeling it as a point source. A point source would make it just a matter of length, but when it's not a point source you can't help but get overlap between two "points" that are close enough together, because they both will be lit up at the same time, no matter how long the tube may be.

[Eridrus]

Ah, I think you're right.

Though the intensity would fade as the sun moves, so maybe you could potentially have some sort of intensity filter?

[grandalf]

Perhaps a nighttime version intended to work with starlight would work. It could be aimed at Polaris and combine the light from all the stars swirling around it to project the digits.