People are always the issue. But I take your meaning.
Indeed in the 1930s the dust bowl exodus was by people who were farmers, or from towns and cities who's existence was 100% dependent on agriculture, for food and employment. At most this exodus was numbered in the thousands, not millions or anything. The 1930s dust bowl crisis (including the weather and horrible storms) was caused in large part by soil erosion, not from the drought itself per se. There was no irrigation. The drought triggered it no doubt, but it was the farming practices of the time that brought it on. Once this was realized and tillage techniques were altered, things settled down and droughts, though bringing crop failures, no longer bring the dusty conditions that were common in Oklahoma in the 1930s. If you've ever seen pictures of the dust storms back then, it really was truly apocalyptic-looking, and very frightening.
Things are very different in CA today. For one, the issue is not about soil erosion causing weather patterns and dust storms. For two, if and when CA does run out of water for agriculture, there really will be an exodus, but only from farms and agricultural areas, probably numbered in thousands, not unlike the dust bowl exodus in the 30s. Modern western living brings in foods from all over the world, so people living in a city in CA are, except for state-imposed water rationing, completely oblivious to the devastating effects of drought.
So all's good, right? After the final crisis, farmers will all leave and all that water will become available. And at only a 2% loss of the state's GDP. Win win. Very sad, but when it comes down to the bottom line, this is probably what will happen. Only the total loss to the GDP will be somewhat higher than 2% because there's an entire sector of the economy around agriculture that also generates its own part of the economy, including laborers.
The problem is that across the world, vast amounts of water are required for growing food, and this is not going to change anytime soon. Human survival depends on this. As a farmer myself, I get very discouraged at how out of touch people are with the food they eat. They have not idea where food comes from. Grocery stores stay stocked regardless of local, regional, or even national conditions. Rich people can continue to buy organic, as one person put it, "because [they] care," though they aren't sure what it is they are caring about. Food prices are lower than they've been in decades compared to incomes, but that's contributing to things like growing almonds when more traditional food staples could be grown.
California used to grow grains and other commodities before irrigation was developed. Probably farmers will return this way, but the amount of acres required to make a go of this is quite a bit higher than with vegetables or almonds, so we'll probably see far fewer farms survive, and they will have to be much larger.