Well, the Italian Communist Party hadn't done the smart thing and denounced the RB, instead claiming they didn't exist.
This is so terribly wrong. The Italian Communist Party was quite vocal in denouncing left-wing terrorism, and worked to contain and expel its infiltration in the unions.
Some of the more anti-American elements of the Parliament might voice approval,
Nope. Assassination of Moro in '78 had already pushed the mainstream Italian public opinion to turn against far-left violence to such an overwhelming degree that even the legal far-left fringe movements, did not dare express sympathy for the terrorists anymore. It was a kiss of death.
I don't see Reagan taking Communists killing an Army general well, though. Hell, it's not inconceivable to see the US putting a lot of pressure on Italian police or sending in experts in urban guerrilla warfare to work with the Italian authorities.
Most likely, we would see Reagan strongarming the ashamed Italin government into taking closer cooperation with the USA about fighting terrorism. As it concerns the RB, this may mean some US intelligence experts covertly cooperating with Italian police, which would have little effects overall. If the RB kill Dozier, it shall be their swan song, just like the kidnapping was. By 1982, repression by Italian police was already wrecking the RB, they were being arrested by the scores, some of them were turning evidence against their former associates, by 1983-84 Italian left-wing terrorism was extinct as a significant threat.
More interestingly, Italy would be likely forced to take a foreign policy less sympathetic to the PLO and its Middle Eastern sponsors. This has interesting consequences during the Achille Lauro crisis, and perhaps even during the 1986 bombing of Libya.