The short answer is Yes, the two are equivalent. Although "which was" doesn't really help the sentence out any. And I, perhaps unreasonably, hate this sentence a lot.
I think I feel so strongly because we don't even know where his job was. Not to mention what function he performed. He could have been "helping the cooking course in Italy" by editing videos from his mother's basement in Chicago.
After studying physics in college he got a summer job in Italy helping with a cooking course.
This is still a fairly poor sentence because he may have "helped" the cooking course by gathering eggs at local farms. But at least we have him on the same continent now. Unfortunately, but directly to my point, we can't really say more because we don't know what he did. If we take some poetic license we might rewrite it thus:
After studying physics in college he traveled to Italy. There he got a job at the University of Rome selecting recipes for a cooking course offered there.
See a very few more words would have massively increased the information conveyed by the sentence.