It's difficult to say with certainty for every kind of vegetable seed (they're not all identical). However, I can say with surety that domestic tomatoes don't have a dormancy period (at least the variety I tried this with). You can plant them right away, without even drying them (but I recommend doing something to lessen the likelihood of disease first, such as fermenting them). Whether or not they germinate may depend on your temperatures, though. If it's 95° F. or above, they may be less likely to germinate, I've read (and I believe I've experienced that). I would be concerned if you have warm nights and hot days, too, or if it's a constant warm temperature indoors (without a drop at night).
I know from experience that some tomato seeds seem to require more heat (and/or different soil) to sprout than others. My Pervaya Lyubov tomato seeds seemed to be that way (while about 100 other varieties sprouted just fine in significantly cooler weather in an unheated greenhouse in April in worm castings with a little peat moss; the pervaya Lyubov seeds that sprouted were in regular garden soil outdoors when it was between 90° F. and 93° F. outside).
I don't believe I've ever heard of common vegetables needing a dormancy period before planting (but that doesn't mean some won't require one). It mostly seems to be certain cold-hardy perennials that require one (e.g. fruit trees, strawberries, etc.)
I think it may depend on the seed as much as the species and variety, though. I've planted lettuce seeds that took a year or two to sprout, while most sprouted right away. Those were just from a store packet, but it seems at least a seed from each of the two packets of lettuce variety seeds needed a cold period or two.
