Mulch is always a good thing for your soil. Always. Bark chips and other organic mulches won't 'feed' your soil until they are decomposed. Meanwhile they do shade and cool your soil. They sort of pull the landscape together visually.
The reason you might have heard mulch 'starves' your plants (poor terminology) is most mulches are not decomposed and anything once alive and has died is in the process of decomposition. Decomposing organisms use nitrogen as an energy source. So whatever nitrogen is in the soil, the decomposers use it and the plants have to get by with what is left over. While the decomposers are doing their job, all the other soil organisms, if there is no food, go to sleep, go dormant, die. When the decomposers have decomposed some of that mulch, the soil organisms come out of dormancy, eggs hatch, reproduction is fueled. All the other soil organisms outside of the decomposer crews, need decomposed organic matter for energy.
Plants need these soil organisms symbiotically. They help plants to take up the chemicals plants need to make their own food. Plants can survive in a 'dead' soil but they won't be vigorous and healthy. Healthy plants are able to defend themselves from disease and insects. Healthy plants can compete with the weeds. Healthy plants shade the soil and add more organic matter back into the system.
Desert soil is very porous so usually drainage is not going to be a problem. Getting decomposed organic matter into your soil is the most important thing you can do to improve your soil. Heck, the one and only way to improve ANY soil is by the addition of decomposed organic matter. For your soil in the desert it is
Waiting for your wood chips, bark chips to decompose might be all you can do. If I were you I would call my local water and sewer utility to see if they make mulch out of human poop and sawdust. I got spoiled working in Seattle where this was available. It was all I used. Shoot, if a client wanted bark mulch I told them to find someone else. The price was the same! And I never lost a client. I simply gave them references after the big spiel and education and they were sold. I also had a bucket in my rig full of this mulch to let them feel, see and smell. It sold itself.
I'd put this on a new client's beds and in one week (when we revisited) the entire landscape was vastly different. My crews were always blown away, the clients were sold.
The only drawback for this mulch is that it is a bit high in heavy metals. I won't use it in the vegetable garden. But if you ever look at tap water...the heavy metals are higher to include fluoride!
Check your area for the availability of this stuff. If you have access to this you HAVE to use it! Don't get the stuff in bags. I've found that THAT is not the same, hasn't been completely decomposed...P U! This stuff is us humans giving something back that is good...makes us humans look like we belong?
If you can find this please let me know. How large is your property? What are your 'goals'...do you have a vegetable garden? Lawn?
Oh I have to say one more thing. As far as weeds go, putting 2" down on top of raw soil, on top of mature weeds is the ONLY thing I do for weed control. Period. I am not at all worried about weeds. If I don't have this Gro-Co, which I don't here in Central Oregon, I just dump soil on top of weeds or pull them before they go to seed. I got really spoiled by this stuff! If you do have access to this 'product' you are so lucky!! Dump it on top of your soil and you smother weeds, shade your soil, reduce evaporation, feed your soil, improve your soil...and that is all you have do. Of course you will have to replace/add more every other year because this stuff is being mixed into your soil by those organisms who eat it. They mix this organic matter and aerate your soil for you. This human poop mulch does more for soil than...well, any thing else. Your plants will be thrilled. Forget about weed problems. Oh, if you find this product...they will also be able to blow it onto your beds, around your home, around your plants for you...cheap cheap cheap and they do such an incredible job! Dang, I miss this stuff. Wonder what they do with our poop if they don't make this mulch, ummm? I know and I am appalled.