Yes. As with most any medical procedure, there is a chance of infection. If you have your teeth removed by a medical/dental professional they will tell you about the signs/symptoms to watch for. If you have BillyBob or one of his cousins do the job, you would be at an increased risk for complications. 
If you are asking if you can still get sick in general- yes, also.
Please get in touch with a dentist for an evaluation and they will help you!
LinnLMT