I don't think food shortages will be severe. Possibly simpler menus will be needed, rice&beans etc third world style, worst case. But not desperate shortages.
Personally I'm stuck in town with adequate delivery service available from several supermarkets. And being California, much of what's sold here is grown here. But I think shipping all over will continue.
I phoned over to the contractor who prunes, discs, harvests my orchard to see if he and his crew are ok. He replied no changes. He has a bunkhouse and maybe ten laborers there plus a few intermittent workers from nearby. He said work is progressing normally like any year. I think the crew is pruning in his vinyard at this time of year. He had 6 and then 8 working steadily for nearly two weeks in my orchard pruning when I departed there mid-March, after the lockdown was declared. In summary everything is normal for my apple crop and likely his wine grapes.
An interesting statistic I saw recently, half the farm labor in the US is undocumented. I hadn't realized it is that high. Around here its mandatory for a new hire to present ID and SS card plus if his English doesn't sound like he attended a US high school, then naturalization papers or a green card that are persuasively credible as a minimum, to keep the employer out of trouble. So nobody's undocumented, at least at first impression. These are the guys picking your food, let's hope they stick around.