Yes you can get sick from undercooked brats.
Brats that are no cooked all the way through could contain bacteria including botulism and salmonella that could make you sick if you eat the brats when not fully cooked.
When cooking brats you should make sure the brats are fully cooked to kill the botulism and salmonella that could be potentially in the meat.
Eating undercooked or raw brats or pork can also lead to Trichinosis.
Trichinosis is caused when meat is infected with the larvae of a worm called Trichinella spiralis.
Heating and cooking the brats and other meats to at least 165 F kills off that larvae and other bacteria.
So if you notice your brats or any other meat is not fully cooked then cook it some more until the brats are fully cooked.