It would have been better if you had clarified that you meant normal bleeding or menstrual bleeding or normal bleeding. The answer would vary for both.
If we are talking about menstrual bleeding the answer will be a YES. Lack of sleep causes stress which in turn disturbs the hormonal balance in the body. This, in turn, can cause menstrual blood flow.
If we are talking about bleeding in general, like that induced by trauma, then the lack of sleep cannot prolong the bleeding time unless the concerned person is suffering from any blood clotting disease. Otherwise, stress and sleeplessness cannot have a significant effect on bleeding.