Yes, orange groves were once common on the Alabama Gulf Coast.
Postcard Back: "The Satsuma is a Mandarin type, "Kid-glove" orange of delicious dessert quality. It was introduced into the United States from Japan in 1876. Satsuma oranges are grown extensively in the Gulf Coast section. Single orchards in Mobile County comprising as much as 1100 acres." Postmarked 1947.
There are still some trees scattered about in Orange Beach. Here is a picture that we took earlier this year of a satsuma tree in a front yard.