Should I leave it in the sun for a few days / weeks before finishing it
Given the right conditions only a couple of hours is apparently enough to replicate the natural indoor ageing of cherry over some years. But others living at a more northern location might need to leave the wood (or the finished project) exposed for longer. Here are some test pieces exposed to "direct sunlight for two weeks", bare and with various finishes on them:
[Source: this thread on Woodweb (see note bottom about chemical ageing)]
or will it still react with UV under a finish (assuming no UV blocking finish) and darken again naturally?
As you can see from the above the effect appears to be accentuated under finish rather than slowed in any way (as you say, assuming no anti-UV agents in the finish).
Also, does the answer apply to all types of wood?
Very much not. Usually the effect is a little slower but the same direct sun that attractively darkens freshly-worked cherry often will have a negative effect on other woods.
Just very broadly, lighter woods tend to darken with UV exposure and darker woods will tend to be bleached.
The bleaching effect is especially notable with woods that are any sort of reddish colour, the natural compounds responsible for this colouring in plants are not lightfast and you can get significant lightening and an almost complete loss of the vivid colouring that makes the wood special.
A particular example worth noting is purpleheart, UV exposure will cause the colour of purpleheart to change to its default meh brown colour. But actually this is common with all violet-hued woods, none of which retain their colour indefinitely. So, if you want any violet colouring on a project you should rely on dyes and not on the native colouring of the wood. In addition to having much more confidence that the colour will remain as you intended it to be another advantage this offers is that you can use a pale-coloured wood as the base that will often be much cheaper.
If you would like to experiment with chemical ageing of the cherry, there's no reason to use anything remotely as dangerous as potassium dichromate. Common household lye of course is also a hazardous chemical if used carelessly, but good news is that similar colour changes can be possible using other mild bases. The two most common that people experiment with are simple household chemicals: baking soda and washing soda.
Even in pure form both are safe for direct skin contact so these are much more user-friendly to play around with in the shop.