It would need to be a real big exodus for property tax revenues to go down. Prop 13 limits and associated low turn property turnover means a large amount of the tax roll is assessed under current value. During the 2008 real estate crash, few of the California counties saw a decrease in property tax revenues.
Probably yes, however, because so many properties are assessed so far under their current market value, due to historic low turnover, the high turnover of an exodus would tend to raise the overall assessed value, unless the price drop was very extreme
