If fartus is to be understood as "full after a good meal", translation is correct. However if we understand it literally (which leads to funny comments about anthropophagy), or even as a way to mock poor Marcus (overweighed Marcus?), then I think: Num Marcus caseo fartus est? should be accepted.
Thanks for your comment. However, I'm not concerned about the translation, thus I won't take into consideration, at first, the "daughter languages". The point I'm uncomfortable with is the phrasing in latin, where the use of fartus is only literal. Hence, the only way : Num Marcus caseo fartus est ? Regarding, now, the "daughter languages", I would strongly recommend not to use "Je suis plein" in French or "Sono pieno in Italian in any situation you mention. In French, it would be considered rude or at least vulgar. Except for "être plein de soi-même", to be full of oneself. It makes sense, of course, in English, which I would describe more as a "step-daughter language". If anyone knows an instance of a non-literal use of fartus in a Latin source, I would like they share.