As this inquiry appears more related to diving medicine than "the scientific aspects of decompression," the focus of Ask Dr. Decompression, I have taken the liberty of moving it here in the hope it will generate more responses.
To the best of my knowledge, there has been no study of nicotine gum & scuba. However, those with a history of heart or circulation problems, such as an irregular heartbeat, chest pain, heart attack or high blood pressure, or of stomach ulcers, overactive thyroid or diabetes, should not use it whether topside or u/w.
Side effects of such nicotine replacement usually are mild to nonexistent at recommended doses. Symptoms such as racing heart (and abdominal pain/nausea, vomiting, diarrhea, dizziness, visual/hearing abnormality, significant headache, flushing or confusion) generally only occur in very sensitive individuals or in those who are taking too much.
Obviously these could have implications for safe scuba, e.g., racing heart contributing to diver panic, visual/hearing abnormality, headache & confusion being confused with DCI.
The student should carefully monitor his or her use of the gum and reduce intake if signs/symptoms of overdose are evident.
Best regards.
DocVikingo