Yes but... evidence like this is hard to acquire - the most you can get is convincing circumstantial evidence (if the phone survives get accelerometer and activity use from it. That sounds like a worthwhile branch of forensics)
And even if we do it's hard to go from circumstantial to causal
But as a driver, I can (un)happily attest that I am distracted from the road if trying to do anything non trivial with my podcast app (the only thing I will let myself use)
Having physical on steering wheel buttons will reduce this but not end it.
Perhaps we just ban radios, phones etc as a precaution.
(Ok actually we can do an experiment - force 50% of drivers to never use a phone or similar and 50% donwhat they like. See who's dead after six months)