in my experience not, I've been trying to squeeze 2 generations in this winter to make some seeds, so I've been trying to germ some really fresh seeds.
my experience with those seeds has been they do need to rest/dry for 1-2 weeks after coming off the plants. seeds less than 1 week off the plant wouldn't germ at all, with 2 weeks old seeds there were still a few non-germers but most germed, without any cold treatment.
could be some variation among strains though, I expect most common (cultivated/domesticated) strains will have very little dormancy, but maybe more wild landraces/feral populations might need longer, and maybe some(I would expect mostly from russian/northasian ruderalis, from areas where there is a clear winter) might need cold treatment too.
but usually I do store my seeds(after drying for a few weeks) in the fridge, so they get a cold treatment wether they need it or not.