Furthermore a huge aspect that isn't present in tests, but is present in CTF (and some other) gametypes, is being aware of your opponent's movements. You also need timing when it comes to collecting key items (Cs>PUs>ammo).

When talking about the most 'popular' tests (aka jumping past warps along solid tiles). They do in fact train small, quick movements which might help you in some places, such as coming up from the right warp area in semi with speed.
Either way, tests involving RF climbing can sometimes give finite training for reaching some high places in certain levels of other gametypes (like the bases in semi).

The somewhat rare 'RF jumping' tests might help you train horizontal movement speed in levels where RFs are present. This could also be of help in certain races with open, horizontal parts (and is necessary to use the shortcut in Rag's Mystic Isles -race with Spaz, at least).

Tests where you need to avoid or manipulate springs, require (jazz-> <- spaz) morphs, seek the right path through a maze (especially the ones that aren't visible) or that involve other such typical test 'skills', won't help you become a better CTF player.

The bottomline is that certain tests can make you better at certain elements that are often rarely present (or at least rarely useful) in CTF or other gametypes.