yes :) . I also seem to remember that years ago in an English to Italian phrase book in that section they used to euphemistically call "socialising" or whatever there was the Italian for "what time is your last bus", presumably so that the speaker could accidentally on purpose arrange for it to be missed.
The English term "partitive" is sometimes used for expressions like "some fruit", as in, for example, "I have some fruit." In question form this becomes "Do you have any fruit?" However, as you say, it may not be an actual thing: when no word is used, the "some" (or equivalent) is implied, so "I have plans" means "I have some plans". (In fact, in this example, you don't normally say "I have some plans", although "Do you have any plans?" is fine.)