I'm not a banker and some banks have different rules and regulations. But for the most part, if you have made arrangement with your mortgage company to have automatic withdrawals then it is your responsibility to make sure that funds to cover the amount are available. Should there not be enough funds to cover your payment then YES it will cause an overdraft. The only thing that may help is if you have overdraft potection or your bank may pay that amount as a courtesy. However, you will also be charged an overdraft fee. Which is probably a nominal amount for allowing your mortgage to be paid.
When you have your mortgage payment set up for automatic draft from your account, the bank will automatically draw the amount when due. If there are not sufficient funds to cover the payment, you will be charged an overdraft fee. They will try a second time to withdraw as well, and you will be charged a second overdraft if the amount is still not enough to cover the payment.
A couple of suggestions on how to avoid this:
1) cancel the automatic payment of your mortgage payment
2) continue with automatic payment and add overdraft protection to your account. Your bank can help you with this.
3) continue automatic payment and request that the date for drafting the payment be changed to 2 days after your paycheck is deposited.
I hope this helps.
Talk to your banker as he/she may have other suggestions for you.