Bad Tomatoes can indeed make you sick because when tomatoes go bad they can contain bad bacteria.
Eating bad tomatoes that are actually spoiled can cause abdominal pain, stomach cramps, diarrhea, vomiting and even food poisoning.
It's unlikely that the bad tomatoes would kill you but you will fee really terrible if you do consume bad and spoiled tomatoes.
If the tomatoes have gone soft, smell bad or they are changing colors then throw them out.
It's not worth the risk of getting sick from bad tomatoes or other bad food.
Fresh Tomatoes last for about 1 week on the counter and in the refrigerator the fresh tomatoes will last for up to 2 weeks.
Bad Tomatoes will usually grow mold, get wrinkly, soft and sometimes smell bad as well.