Yes, they can be faster. A dead stiff frame seems to bog down and get rattled on rougher roads, where a quality frame with some designed in twang will shrug off the high frequency vibes, will carry speed better (micro levels of better) but will also leave you less beaten, so you can be faster for longer. Also consider weight savings will allow better acceleration.
I ride a ritchey logic steel road bike. It handles back roads very well.
Stiff bikes are great for power transfer and sprinting. But if you don’t pay your mortgage with race winnings… Why worry. The only sprint that counts if you don’t compete is the one against your mates to the pub. I would prefer a frame with more character and buzz handling qualities.