Tried googling it to see if there was any players from a few decades ago - i had heard of Giovanni Moscardini who was born and grew up in Scotland but later played for Italy and scored for them in the 1920s. He played for Lucchese and Pisa but it seems neither were in Serie A at the time.
Anyway another player of interest that came up even if he didnt score in Italy was William Aitken who played for us 1918-1919 then went onto manage Juventus 10 years later (would have played for them too if foreign players weren't banned then). Not only that we had another player in the 1920s called Billy Chalmers who went on to manage Juve too! Not sure if this is common knowledge but i'd never heard of them before and that is quite a link to one of the giants of world football.