That is correct. Entertainment and food techs will be bought by synthetics, it won't get added to their list, and they will buy the same techs the next time you speak with them. In fact, even cycling through civs in the trade screen back to the same synthetic civ, will place the techs tradeable with them again. One can wipe a synthetic out of money, techs, resources, and starbases, in a single turn, trading them same techs over and over.
It also works on silicon civs, with higher food techs (so long as it doesn't appear on their tech list).
Sorry if my initial post wasn't super clear.
(edit) When trading, you can tell which techs this will work on. The "number of turns" on the tech mouseover (in your technology list) is blank.