apt (and all programs on top of apt like HAM and fapman) works like this: referenced by a sources.list it grabs some informational catalogues form specified repositories and builds some kind of lokal database out of them. This lokal database you can use as long as you want to but it is only as actual as your last update. Therefore it is usable for offline searching in the database but you will not see newer updates until you re-download the catalogues again (e.g. run the update).
Upgrading instead means bringing an installed application to a newer version. This requires in first place to have an updated database of available applications (e.g. having run the update). Of course, for updating as well as upgrading you need a connection to the internet.