Pretty confident the answer is no. People who were just evicted from their farm, and had all their possessions sold at auction and applied to their debt to the bank, didn’t have money to buy train tickets to California. They drove if they still had a car or truck, rode freights, or walked. California had border guards who would turn back anyone who didn’t look like they could support themselves - which was part of the inspiration for Woody Guthrie writing “This Land Is Your Land”.
As far as photos, I think this famous one sums it up…
p.s. Although it was worst in states like Texas and Oklahoma, the Dust Bowl affected a huge part of the U.S. My mother remembered that for a time in the 1930’s all the kids in her school in Minneapolis MN had to bring a wet rag or towel to school with them from home, because even with all the school’s windows and doors closed, their desks would be covered in dust that had blown in overnight.