Depends on exactly where in LA you are, but yes and yes, to your questions. Our first house didn't have AC, and adding it (plus central heat) was the best 12k I've ever spent.
if you live near the beach, not really necessary. when we lived in Santa Monica, the ocean breeze was enough and it rarely really got HOT hot. we now live in the Beverly Hills area, and I think it's a necessity. I haven't turned it on yet this year, but it definitely gets constant use come late july, august and into september. we used to live near the Grove and didn't have a/c, and there were days in the summer that it would be in the 90's inside our place. if you're in the Valley, you definitely need it. one of the requirements when we bought our house was that it have a/c and central heat. and I would definitely add it to my home if it didn't have it already.
I'm in North San Diego County, but we are about 1 mile from the beach & it isn't necessary. Our house is also heavily shaded & the ocean breeze flows right through when the windows are open versus hitting the side of the house.
Our last house was about 6 miles from the beach, had no a/c and it was absolutely miserable.
We live about 10 miles from the beach, west of LA, and wouldn't need AC if we could open windows, since we have breezes off the ocean. Unfortunately, our neighbors have barky dogs that they leave outdoors all day and we have one reactive/anxious dog who doesn't do well hearing them, so we have windows shut, and a window AC and a portable AC unit.
I would definitely upgrade and add AC. It used to be that there were only a few weeks in August and maybe Sept/Oct, that it might have been nice to have it, but it has been much warmer and more often in the past few years than it was when we moved into this house 19 years ago.