You may be able to add some digital rain in wide shots, but for closeups if you don't see rain interacting with the stuff it hits and bouncing/dripping off umbrellas and people then it won't look real.
Plus, all of your actors will be dry.
We just did a rain scene that was so far away from a water source we couldn't use a cheap rain machine. We filled 10 5gallon buckets with water, carted them to the set and stuck a guy with a watering can above the actors. Drenched everyone on screen and you see enough water bouncing off everyone that the extra we add in digital is going to blend nicely.
You could wait for a rainy day.
Or, just don't have it raining in the scene?