No! Leather will start to break down when it gets wet and stays wet for extended periods. You should try to avoid showering or swimming whilst wearing your leather strap.
Allowing to dry to a damp state then applying leather conditioner is one way of preserving your leather watch strap. Best to not get it wet in the first place. Note: you will void any warranty if your leather strap gets wet. We would also advise you not to swim whilst wearing a watch even if it says it is waterproof.