Jupiter, Venus, Sirius and, at the very limit, even Canopus are visible with the naked eye during the day. It's just hard to "get a lock" on them because contrast is so low. But if they are close to a large, fixed, easily visible reference (the Moon, a tall building, a tree) then suddenly they pop into view. The first two are easy, the third is doable in good conditions, the last is difficult and requires excellent conditions and a keen eye.
You need more than a few stars for navigation, of course, but I would assume with a good sensor, proper filtering, and nice optics, a computer could see enough stars during daytime to perform navigation.
The IR filter helps, but (this is sort-of speculation because I don't have any knowledge of the system outside of reading the patents), I think the major processing gain comes from the shutters. In fact, I think the patents said that it could work (albeit much less effectively) without the IR pass filter.
The basic idea is a form of synchronous detection or lock-in amplification: The shutters are arranged so that a point source is occluded at a fixed frequency, while an area source will be only partially occluded at any given time. Due to the way it is designed, area sources should add little to the time-varying component of the photodetector signal. The lock-in amplifier is essentially a very narrow notch filter (centered at the "star occlusion frequency"), so it completely rejects the DC component from the sky.
There is a little more to it than what I'm writing, mainly because you need to not just detect the point source, but also estimate the star's position within the field of view (which IIRC is done by comparing the phase of the time-varying star signal to a reference point on the shutters).
