No, it does not.
To research this question I had to wade through a huge number of fringe articles, many of them identically worded to the one above. It took me a while to find a reputable news organization. But eventually I did..
Can I still share (and sell) vegetables from my garden?
Yes. Farmers who sell most of their harvest directly to restaurants, food co-ops, farm stands, and farmers' markets wouldn't have to register with the FDA under SB 510. And they wouldn't be subject to the regulations in the legislation. But such farmers would still have to abide by current state laws.
That's not to say the bill isn't controversial. Many people are opposing it on the grounds of increased regulatory burden on small food producers and sellers. Many people are supporting it since it holds food producers responsible for contaminated food, and makes it easier to track the source of such food. But in the specifics of this question, no. As one article puts it, Grandma's home grown pickles are safe.