Can confirm this is not always the case, in fact you're likely to experience the opposite. Source: became father 1.5yrs ago.
If you are the mother you're more likely to experience postpartum depression. Even fathers experience depression. I have had to work full time, do household chores on top of keeping the baby happy, who didn't sleep well at all at night and even now does not. You're going to miss deadlines, fail to meet expectations, do lousy job of your assignments. All of that will or will not affect you, physically and/or mentally.