No they don't need light to germinate but as soon as they emerge you better have light over them or they will immediately get leggy with weak stems.

Considering you are suposed to plant the seed 7-13mm and light really only penetrates dirt around 4-5 mm... tomtoes and peppers already germinate without light. But as has been said, they do need light from the time they emerge, so many gardeners start them under the lights and just leave them there as they emerge into the light. Or put them under lights as soon as they emerge.

The plants themselves don't need any light before germination. Photosynthesis happens in the leaves. But strong lights aimed at the surface warms it up, which those seedlings love. Even with heater mats down below, the surface is the coolest part of the pot, because of evaporation. I always keep pre-germinated seeds in soil under lights for exactly that reason.