Seems they don't from my tests but just to double check. My setup is made up of a few objects marked as static, all sharing a standard shader material with some emissive color, GI set only to precompute and a realtime reflection probe (set to render on every frame) attached to the player, which is the object that moves and passes near the emissive objects. The player has a metallic material, also standard shader-based.
In the editor, this generates reflections on the player as it passes near an emissive object, as you'd expect.
On iOS, the player looks dull, very dark, and no reflections appear on its surface.
I also tried setting instead the probe to Custom and tell it to render from within a script, since I can't just pre-bake the probes, because the static objects are brought in at runtime. This doesn't seem to work either: the probe doesn't seem to render anything.