Yes, sulfur is an essential plant nutrient and a deficiency will undoubtedly have detrimental effects. However, I can't really follow your logic on it's use in the germination process. Merely stating what happens in a deficient state is not in itself merit or evidence to prove that sulfur is required for germination. Although you state that plants are commonly deficient of sulfur in aquaponic systems, this has nothing to do with seed germination. Adequate pH and temperature are the key factors to getting a high germination rate. Since the seed embryo contains everything it needs to germinate, it really does not rely on nutrient uptake through the seed coat to germinate nor is it deficient. So, what would help pepper seeds sprout? Adjusting the pH and temperature.

Yes, having an optimal level of nutrients will help a plant in the "early stages of development" and the rest of its life cycle. This is not in question, but again, I am trying to draw a distinction between the germination of the seed and the rest of the plant's life cycle, as you mentioned, to answer the original poster's concern of germinating pepper seeds. Please keep in mind, nutrient uptake from the soil does not occur until AFTER germination has occurred.

Now that that is cleared up, I did not know that plants absorbed foliar spray nutrients through the leaf epidermis. Is there any chance you have "recent research" or recall where it was published?? I would like to read it. I have been taught that it only occurs through the stomata, but a brief google search reveals some evidence to what you are saying; however, my references keep leading me back to a commercial webpage selling chemicals for foliar applications. I will keep searching since I was even taught this recently in my Master Gardener training by county faculty. It is definitely something to correct for future curriculums. Thank you for that, this is why I love this forum!