Incredibly doubtful. Your son is an adult and is responsible for his own conduct. You have been kind enough to cover him under your insurance. Your son can get sued and the person who allowed him to drive the car under the influence can be sued (if they knew of his state). However, you are likely not liable. As with any situation, we see people improperly sued every day. So, you can actually be sued. But, I simply do not see exposure to liability in your situation
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice.
Being on the same policy does not make you liable for an accident.
I am a personal injury lawyer located in Dayton, Ohio. I am an experienced trial lawyer who represents injury victims against the insurance companies. We do not have an attorney-client relationship. I am not your lawyer. I am not providing any legal advice. I am only licensed in the State of Ohio. You should contact an attorney for legal advice.