Unless you absolutely can't/don't want to get to DCA until after noon or you actually want to eat the picnic, I personally would not bother with the picnic, off-season or not. FPs should be easy to get and it should probably only take a few minutes. If you arrive at DCA's opening (30 minutes prior to listed opening time), you should most likely be able to get blue, and I understand the picnics give yellow (considered a lesser section, though there are still some good spots).
In the off-season, and maybe even in the on-season, they will probably be giving out yellow or better FPs until at least noon, and quite possibly a couple hours (or more!) after that. If you would settle for red you could quite possibly come over at 2 PM or later in the off-season and get a FP.
I don't think the picnic is a horrible value necessarily, but it sounds like it's basically a snack with a FP. If you are at all budget conscious or just don't want the picnic, and if you don't mind hopping over to DCA to grab a Fastpass, there's really no purpose to the picnic.