gettarsi a capofitto sul lavoro
{or}: gettarsi a capofitto nel lavoro
The equivalent French expression "se plonger dans son travail" invariably employs the preposition "dans" corresponding to "in" in Italian. The same goes for "throw yourself into work" in English; you never say "throw yourself onto work".
A few bilingual dictionaries that I have consulted have it as "gettarsi a capofitto in ...". The thing is that I came across "gettarsi a capofitto sul lavoro" in an email message professionally translated from English -- and written in a colloquial tone. As such, I figured it was unlikely that a grammatical error like this would slip in.