Possibly not.
It was a bit more complicated than that. The 'Italienstau' had existed since the first movements of Sperrverband Rommel to Africa and was made up of all sorts. It also wasn't all in Italy. When the Tunisian capitulation was near only about 5,900 men of Division 999. had reached Tunisia, only 1,146 were in Sicily and another 9,213 were still in France and Germany. Thy were the primary source for Division Sizilien, along with six Marsch-Batallionen that had not gotten to Sicily and some convalescents and men on leave from 15. Panzer-Division.There were actually only four German divisions there:
1, The 15th PzGrD, which was the renamed Division Sizilien, made up of troops destined for Tunisia, but still sitting in the "Italian traffic jam". No Tunisian campaign and evacuation in late 1942 means no "Italian Traffic Jam" and no Div.Sizilien and no 15th PzGr.
Um, if the division did not send any troops to Tunisia, then it would have all the troops it had in July 1943 plus those it lost in Tunisia.2, PzDiv Hermann Göring: It was formed from the parts of Division Hermann Göring that stayed behind in the West when parts of the same division were rushed (and destroyed) in Tunisia. If Africa is lost already in 1942, and Husky is done five months earlier (February or March 1943), it is doubtful, if the division would have more troops, than what was sent to Tunisia OTL
Actually it was only renamed as 29. Panzergrenadier-Division on 23 June, it was already 29. Infanterie-Division (mot). That unit was reborn on 1 March 1943 by the renaming of 345. Infanterie-Division, which in turn had been organized 24 November 1942 and had already established a Panzergrenadier Brigade for employment in the east, although it was not deployed. So it was actually re-raised about seven months earlier than most figure., 29th PzGrD, was only re-raised in June 1943, after it was destroyed in Stalingrad. We can disregard it against any landing, that would be done earlier, than OTL-Husky
True, but it was 30 March when the division began moving west. Then there are whatever elements of Brigade Ramcke that can be evacuated and 5. FJR that likely wouldn't be sent.4, 1st FJD. The constituent units were only collected from the Ostfront in May and June 1943, and was rushed to Sizily after the landing. We can disregard this division for any earlier landing too.
Um, as of 1 December 1942 the ration strength of the German elements of the Deutsch-Italienische Panzerarmee numbered a bit more than around 5,000 men. It was actually 40,674. If the resources used to move 5. Panzerarmee to Tunisia were utilized to evacuate rather than to reinforce, then it is likely most of those would escape.Then, there are the divisions destroyed in Tunisia, namely
I, Ex-DAK-troops:
1, 15th PzD
2, 21st PzD
3, 90th leD
4, 164th leAfrikaDiv
5, Brigade Ramcke
All these together had around 5.000 men, 35 tanks, and a dozen or so field guns. Even if they could have been evacuated from Tripoli in December without further casualties - doubtful - this wreckage wouldn't be much of a reinforcement for Sizily.
I do not recall seeing anything indicating that Regiment/Brigade/Division Hermann Göring was ever scheduled for Africa prior to TORCH?II, 5th PzArmy troops:
1, 10th PzD
2, Division Hermann Görig: see above
3, 999th AfrikaDiv
4, 334th InfDiv
From these, only the HG and the 999th were scheduled for Afrika even before Torch, so they may find their way to Sicily after the evacuation from Tripoli in December. The other two... without a new front in Tunisia to be built up in late November, it is quite likely, they would be sent to deal with the other trouble brewing in late November elsewhere. Please note, that the units, sitting in the "Italian Traffic Jam" from all four Divisions were used to magick up Division Sizilien (aka 15th PzGrD) and a Div HG was on Sicily OTL too.
"999th AfrikaDiv" see above too. BTW, it was established 1 February 1943 as leichte-Afrika Division 999., so technically was not scheduled for Africa prior to TORCH, only its predecessor Brigade formation was.
However, everything I have seen says that 334. Infanterie-Division was established on 25 November 1942 with the intent of using it as an Africa reinforcement.
It really comes down to timing of the decision to evacuate Africa. If the fait accompli of TORCH and El Alamein are recognized, then quite a bit could be left on the table for use in Sicily, Sardinia, and Italy.