The 1st US Army infantry division fought in Operation Torch, Tunisia and Sicily. It also landed on Omaha Beach on June 6th 1944.
The 3rd US Army division also fought in North Africa, Sicily and Italy, before being used in Operation Dragoon, the invasion of Southern France.
Yes it was. Many US infantry and armored divisions and other units served in multiple theaters during WWII. The 3rd Infantry Division was the only US division to fight the Germans on every front in both the European and Mediterranean theaters (North Africa, Sicily, Italy, France, and Germany) suffering more casualties than any other division. The following divisions that served in Western Europe served in other places before then:
| Division | Campaigns before the ETO |
|---|---|
| 2nd Armored Division | Sicily |
| 1st Infantry Division | Algeria-French Morocco, Tunisia, Sicily |
| 3rd Infantry Division | Tunisia, Sicily, Naples-Foggia, Rome-Arno |
| 9th Infantry Division | Algeria-French Morocco, Tunisia, Sicily |
| 36th Infantry Division | Naples-Foggia, Rome-Arno |
| 45th Infantry Division | Sicily, Naples-Foggia, Anzio, Rome-Arno |
| 82nd Airborne Division | Sicily, Naples-Foggia, Rome-Arno |
Many tank and tank destroyer battalions and other non-divisional units also did the same.
As the Ranger battalions only accepted volunteers, T/Sgt. Horvath could have previously served with one of the above divisions, most likely the 1st, 3rd, or 9th Infantry Divisions (given cans labeled Africa and Italy), or some other unit that fits the criteria of having served previously in Africa and Italy. Assuming the actor's (Tom Sizemore) real-life age at the time (37) was the age of his character in the film, and taking his rank (Technical Sergeant) into account, it would seem likely that he was a career soldier. He would have had to volunteer for the Rangers at some point after fighting in Africa and Italy, probably sometime in late 1943. As an extra tidbit, the organization of a Ranger infantry battalion is as follows.
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