Utilization is near real-time. What that means is that what is reported is what is taken in terms of debt-to-income (DTI) ratios. When a mortgage broker pulls your credit, they will pull the latest balances with the minimum payments. This is what is taken to determine DTI along with your gross monthly income. If you do not pay your account in full before the statement date, then you more than likely will have to wait an additional statement cycle before it reports to the credit bureaus. Therefore, your utilization is dynamic and the history of your utilization month-to-month is not recorded forever. Only the current balance. What is maintained and reported is your payment history. So you want to never be late if you want to be approved anytime soon for a mortgage.
A lower DTI will not help your interest rate. As long as you stay away from the maximum DTI for the mortgage vehicle you are attempting to be approved for (VA, FHA, Conventional, etc), then your DTI should not be a concern. If you are borderline at the time of underwriting, you can take the opportunity and pay off the balances. The mortgage company can then do what is called a credit supplement which entails contacting those lenders where you have proven you have a zero balance and manually input the zero balance cards, that have not yet reported to the bureaus, in your final application to the mortgage company for underwriting approval.