No, nearly all of time he wouldn't.

When you die every muscle relaxes including muscles in arteries and veins. That means zero blood pressure.

Imagine a central heating system and suddenly all the pipes round the house became three times diameter and the control panel failed and the pump failed. The water wouldn't go round your house and water would flow out of the radiators.

In the body every artery expanding and the heart stopping means no blood pumpimg into the erection and the veins that hold blood inside your erection also widen and the veins flow out.

The exceptions...

Electrical burns to the gonads which burn muscles, arteries and veins so blood is trapped in erection. That blood will eventually clot inside.

Dying on the job wearing a cock ring or similar. Again the blood will coagulate.

Gunshots to the brain that damage cerebellum. Won't stay forever though.

Hamging and some spinal cord injuries. Won't last forever.