In short, yes. People have been laughing at fart jokes for over 2000 years. And I suspect a long time before that as well. But the first written evidence we have of toilet humour dates to about 2400 years ago.

The Greeks had a form of dramatic play called comedy, alongside tragedy. According to Aristotle, comedy was recognised later than tragedy, probably in 465 BC. Before this time, there already was comedy theatre, but this was performed by volunteers. After its acceptance it was organised the same way as tragedy theatre: before a festival the city would appoint a so-called choregos for each piece that was to be performed. This was a wealthy citizen who would pay for the masks, props, musicians and housing and food of the chorus.

Comedy was known for its bawdy nature. It seems like most jokes revolved around drunkenness, sex, farts and lampooning famous contemporaries. So, not only did the Greeks have toilet humour, it seems like the whole origin of comedic theatre arose from these kinds of jokes.

Aristotle says that the first comedy theatre pieces were by Sicilian playwrights, Epicharmus and Phormis. An early Athenian to write comedy was Crates. But the first comedies we have full versions of are by Aristophanes. In one of his works, The Clouds, he opens the play with a father and his son lying in bed. The father is worrying about his troubles, but the son is blissfully asleep and suddenly lets out an enormous fart, no doubt getting a big laugh from the audience.