Can a person have an endoscopy and colonscopy with thrombocytopenia?

In general yes: But if there is a very low level of platelets the gastroenterologist may be reluctant to biopsy a lesion if found.

Not usually: The risk of bleeding increases with decreased platelets. If the study is urgent and platelet transfusion can be sometimes be performed prior to the procedure.

Count: It depends on your platelet count. A platelet transfusion would likely be advised prior to a colonoscopy with a count of less than 10, 000 platelets. Otherwise, it should be quite safe.