If a person does not have t.B could that person cough up blood if he coughs too hard?

Yes. There are many reasons someone may cough up blood. Other bacteria can cause bloody mucus other than tb. Most commonly, is strep pneumonia.
Not really... There are many disorders that lead to coughing up blood, or hemoptysis. Bronchitis, pneumonia, malignancy are a few disorders that can lead to hemoptysis. This symptom always needs to be evaluated by a physician to determine its cause and provide treatment. Coughing hard, per se, does not usually lead to hemoptysis but whatever is causing the cough is most likely the cause of the hemoptysis.