I did not find the name in Broadfoot's list (Roster of Confederate Soldiers), but this name lends itself to a variety of misspellings. I tried those I could think of, but without success.

Also tried the Roster of Union Soldiers and found the following possibilities (just in case he may have been a Yankee):

Gustafson, Charles IL 19th Inf. Co.H
Gustafson, Charles IL 52nd Inf. Co.K
Gustafson, Charles IL 66th Inf. Co.C
Gustafson, Charles IL 127th Inf. Co.C
Gustafson, Charles MN 3rd Inf. Co.D

(none of these from Alabama, obviously)