The answer to this question can never be generalized for it largely depends on the products that are used for teeth whitening. It is worthwhile noting that many of the modern products have neither shown adverse effects on the teeth nor gums, but your dentist would be the best person to decide on this issue. Dentists advice against teeth whitening if you have a gum disease, are pregnant or nursing the baby, and when you have tooth colored caps and other dental work that has been done on your front teeth; as these front teeth cannot be bleached.
Generally high concentrations of tooth bleaching agents in the past caused increased sensitivity. But with gels used for bleaching being now less concentrated the sensitivity is now reduced to just 48 hours after bleaching. The sensitivity can also be considerably reduced with brushing with toothpastes containing potassium nitrate or fluoride that help reduce sensitivity by soothing tooth nerve and also re-mineralize your teeth. You could also minimize the use of the tray applicator if you are using one, with opting to stop whitening for a while helping in allowing the teeth to adapt to the procedure.