Depends on your orbit.

Earth's shadow can be avoided even in low earth orbit:

https://en.wikipedia.org/wiki/Sun-synchronous_orbit

If you can see the stars, and the sun, is it night or day?

It's a Sun-synchronous orbit, https://en.wikipedia.org/wiki/Sun-synchronous_orbit . There is no time when the Earth comes between the craft and the Sun.

The "can" in the phrase "An orbital data centre can be effectively in your line of sight and it can be relatively close" is doing a lot of work. It's a polar orbit, and over half the time will be over an ocean, and not over anyone at all.

At https://en.wikipedia.org/wiki/MetOp#/media/File:Ground_track... you can see the ground track for MetOp-B, in Sun-synchronous orbit at 817 km elevation, so a bit higher. It also shows the line-of-sight in the egg-shaped white outlined region.

A ground station will need to be within that region (which is large), or a satellite will need to relay via another satellite (adding more distance). In either case, the average latency will increase.

Since consumer devices don't support ground-to-orbit laser communications, there will need to be ground stations. How many are needed to get the latency low enough? Why not replace the ground stations with a compute center?