I sure hope not since I am using Home Depot buckets. I always run a gallon of bleach with 40 gallons water and then 4-5 complete system change outs when adding new buckets so hopefully the system is fully flushed by then.
FDA approved just means that they're not using recycled content when they injection mold the buckets, and that the physical design of the bucket allows for easy cleaning (no crevices or holes where water can collect and bacteria can grow, etc.) FDA approved plastic bucket or not, it's all still HDPE at the end of the day. You'll be fine.
ETA: It's also worth noting that a lot of non-FDA approved buckets would actually qualify for the approval if the company manufacturing it bothered to get it certified. Sometimes it's not worth the time and money.