Nope, it rains for me randomly more or less, beautiful graphics when it's raining though, the work CDPR have done on Red Engine is amazing
Some of the weather 'types' I have seen so far to give you an idea of the variety if you haven't seen it yet :
Heavy Foggy Rainstorm
Im on PC. Here is what I have found.
I noticed alot during play that the road would become wet like its raining, but there was no actual rain visible many times. Later on I hex edited the EXE to disable TAA to see what the game looks like. This is when I noticed that when the road turns wet there is an extremely light rain effect happening. The rain drops are so tiny and light that you can hardly see them with TAA off, but you can see them. While I had it turned off, I never saw the roads become wet without seeing rain. I am sure TAA is wiping out the light rain in CP2077. After turning TAA back on (unfortunately the game doesn't work properly with it off for some reason) I have not seen the light rain again, just roads getting wet.
Yes some quests does like "Gimme Danger" with Goro. It's always Sunny when you're on the roof (for the view/dialogs with Goro), but after it always rainning.Im not sure if a mission triggers the dynamic weather. i know that in some games that is the case, and before i hit that Judy mission with Evelyn it hadn't rained except in the prologue with jackie.