Absolutely. Too much exercise can overwork adrenals. Exercise is perceived by the body as a form of stress and stimulates the release of cortisol. In general, the more your fitness improves the better the body becomes at dealing with physical stress. This means that less cortisol will be released during exercise and also in response to emotional or psychological stresses. So you want to ease into a fitness plan.
If I have a client who shows high cortisol levels in lab testing, we start very slow with fitness. Exercise reduces levels of certain hormones such as adrenaline and cortisol. It also stimulates the production of endorphins, chemicals in the brain that are the body's natural painkillers and mood elevators.