Can I run Samsung apps (app market from Samsung) without a SIM and mobile connection?
No, the Samsung apps market won't start without a SIM card, because the card is used to determine the country of the user.

There is an App called "Kies Air" which allows you to connect your device to the Kies App installed on your PC over WiFi. But I doubt that you are able to upgrade the OS this way. It's more meant for synchronization (calendar, email, ...) use.

IMHO you need a USB cable to update the SGS, either with Kies or Odin/Heimdall.