Well, coarse mulch that does not absorb much water mostly sheds rain and lets it reach the soil. Big wood chips and big bark chips: yes. Sawdust or bark fines: no. Fines absorb a LOT of water and it might never wick out of the mulch layer and into the soil.
Therefor, use coarse mulch or else a relatively thin layer replenished as needed.
It would be best to believe someone who USES lots of chopped leaves or grass clippings in a dry climate.
I haven't done that. I either have drizzle a few times per week or I irrigate, so what do I know except what I read? Also, the only mulch I use is coarse bark.