Does Dreepy Spawn in Rain?

Spawn rate is around 2% in the rain. Dreepy on the other hand is even rarer and you have to fight it randomly in the grass where one of the ! comes up.

Can you catch Dreepy in rain?

That one is a standard Overworld encounter so you'll see it appear before you engage with it, and it has a 1% chance in Overcast and Rain, and a 2% chance in Heavy Fog and a Thunderstorm. Not much better, but at least you can look for both Pokemon simultaneously.

Where can I find Dreepy?

The only place that you can find Dreepy is in the Wild Area, more specifically the Lake of Outrage subsection in the upper part by Hammerlocke City. Crossing the body of water you will see a tiny patch of grass that wild Pokemon will spawn in.