"Hey, what's the deal with bathhouses? Is it a bath, or is it a house?"
I can't address this question directly, but I can speak a little about the nature of comedy itself, how it has changed over time. Would what the Romans find funny be still funny to us in the modern day? The short answer is - yes.
I mean probably not everything is a knee-slapper, some stuff is probably so contextual that it'd be meaningless to us today. It was also a crueler time time, as puerile as some of our modern entertainment can be, we'd blanche at watching criminals being fed to animals as the half-time show at a gladiatorial game.
All those caveats aside, there are comedy plays that survive down to this age that are pretty damn funny. The Casina by Plautus has a doddering old master planning to marry a beautiful slave girl to one of his lickspittle slaves so he can have unfettered access to her (without his wife catching on). Another servant who's more loyal to the wife plots to frustrate him. High and low brow comedy ensues and the old codger is humiliated by the wily slave. If you take the foolish master and clever slave trope and port it into the modern day... you get Blackadder III. And Plautus wrote during the time of the Second Punic War down to the Macedonian Wars, what later Romans would lament as 'the good old days'.
And this type of comedy was just one type, we know there were other forms such as comedic plays but, as I understand it, they didn't survive to the modern time. There is Terrence, another Roman playwright, but the few plays I've read of his bore me to tears (I find Terrence to be the Family Circus compared to Plautus' Calvin and Hobbes).