Unfortunately, it did. It suffered horrendous casualties in the Greek counterattack after the battle of Pindus into Albania - many Italian historians used it to justify its horrendous behavior. A large number of Julia soldiers perished when British subs sunk their transport ships ferrying them back across the Adriatic.
After the collapse of the ill-fated expeditionary corps in Russia the reconstructed division fought in the Balkans until the Italian surrender in 1943 when they were disarmed by the Germans.
Incidentally, my paternal grandfatherās teenage younger brother was killed by the Alpini, so I did a lot of research on the topic.
I know that war crimes were committed, mainly by occupation forces which would exclude the Alpini from most of the acts, but the whole fetus thing sounds like post war propaganda. There are letters from Italian troops which talk about killing civilians and burning whole villages. The ripping out of fetuses sounds more like what would have happened between the various ethnic groups within Yugoslavia, such as the Ustashe.
English sources are few and far in between, but in Italian there is of course Eugenio Corti and his harrowing account of the retreat from Don which briefly touches some of this topics in Russia.
That book mentions things that have been documented as war crimes, which were never pursued in court, but I donāt think fetus ripping has ever made the list of crimes.