I don't think it'd be an SAR. They used PBYs for that duty. Or sea planes. Or bombers. Long range stuff. Most likely ground attack if it's got D-Day stripes on.
EDIT: I retract my guess. You appear to be right. Here's a blurb from one sight about the Corgi model
"Originally assigned to the 361st Fighter Group, the "Harriet" was involved in an accident in May 1944, and was classified "war weary" becoming one of the first P-47s assigned to the Air/Sea Rescue Squadron. Coded 5F-G, with serial number 42-75228, this aircraft served with the unit until most of its P-47s were retired in May 1945."
EDIT2:
link If you end up skinning it, there's some more angles shown there.