Does thrombocytopenia lead to a bleeding disorder?

Yes. It depends on the degree of thrombocytopenia. However low platelet count < 20 k are at risk for spontaneous bleeding.Any injury with a low platelet count will result in more bleeding if present.
Decreased platelets. Thrombocytopenia means there are decreased platelets which will increase the risk of bleeding. This is different from blood clotting disorders where there is an imbalance or loss of the proteins that help blood to clot. There are many reasons for decreased platelets but it is important to determine the cause and treat it.