Can a strep throat be cured without seeing a doctor?

Yes: A healthy person should be able to fight infections without use of antibiotics. If you are still ill after a week though, a doctor visit should be scheduled.

Things to ponder: Strep A, like many other causes of sore throat can "get better" without treatment. However, you could be rolling the dice. Failure to treat with antibiotics within 7-10 days of first symptoms can trigger (1/200) the antibody production that leads to rheumatic fever and associated heart disease. It's a major cause of death in the 3rd world. How much risk are you willing to accept ?