Yes, you can. In fact there a whole bunch of ADs out thee regarding exactly that (at least one of the airbus ADs has an active thread I think)
What you do gain is having a (slightly) different means of sensing airspeed, but both are ultimately sensors, in the airflow, somewhere on the nose. That means the are still common cause failures that need to be addressed. The goal is to design those to be sufficiently improbable that a procedural solution is acceptable . i.e. pitch/power tables.