Yes. Your skin is one of the main barriers that stop bacteria getting into your body. If the skin is badly burnt or cut bacteria can get in and cause an infection. Infected wounds can be a big problem in patients with bad burns.
When your skin is burnt it can become broken and so pathogens can enter your body. You may notice that you get a fluid that oozes out from a burn if this is white in colour or has an unpleasant smell then it is a sign that you have an infection and you should see your doctor.