I live in L.A. can I just leave them in the ground all year?
No sense digging them until the early Spring. They do best if divided each year as there will be too many sprouts from the tuber clump and the plants will be weaker. And of course you will have lots more tubers to plant elsewhere. The risks are that they may rot from too much rain(not much risk in LA) or that a critter like a pocket gopher will eat them.
What is a packet gopher?
When I lived in the LA area, I left dahlias in the ground, and they came back for several years. Once in a while one would disappear, but they were out front so could have been human animal for all I know. As long as your soil has good enough drainage, then they should be fine and bloom pretty again next year.
A pocket gopher is a gopher that eats roots and stores them in a pocket in his mouth to be deposited in a food cache. Since he is storing food for the winter, he destroys dahlia tubers in the ground. They are very common in the Northwest and in the Bay area.