Yep! There's the aforementioned short satirical poem by Martial,

In omnibus Vacerra quod conclavibus

Consumit horas et die toto sedet,

Cenaturit Vacerra , non cacaturit.

Epigrams, Book 11, Epigram 77

A poetic translation being given as

In privies Vacerra consumes the hours;

the whole day does he sit;

Vacerra wants to dine,

he does not want to shit

but also such curiosities as tic-tac-toe boards carved between seats, remains of game boards built into the toilets and game pieces left lodged in hard-to-reach places, and various means of 'comfort' such as fountains and mosaics, with 'higher quality' public toilets charging a fee for entry. Wouldn't want to shit with the poors, now! Less relevantly to the notion of socialization, but related to the modern day, there's also considerable evidence for graffiti in the public toilets (including spreading nasty rumors about one's enemies!). More broadly, there are numerous discussions in Roman literature of matters we would regard as, uh, somewhat private, such as the notion of a slave holding his master's chamber pot while he takes a piss, or casual discussion of constipation at the dinner table.

The past is a funny place!