Yup!
You can try lower to experiment (I would). Bonus for running where you and your riding style need to be would be ride. A sign you are too low is if you feel the bike is too hard to pedal, or if you feel the rim hitting the curbs or big bumps. That's a definite no-no. Super hard on tires and tubs.
Depending on your size, it would be no surprise if you found 55-60 worked better for you. Downside here, would be the lack of a "safety zone". Riding after inflating to 70 psi will assure you the tires are properly inflated for a few days. Riding at 55-60 would mean constant monitoring to prevent a "too low" condition.