Hey Atilla!
Thanks for reaching out. Using ActiveSync on Android and iPhone should sync the Global Address List (GAL); however, it will only sync on a search. By this, I mean that you won't see a GAL entry while browsing your contacts, but an entry will appear when you do a search in your contacts list. This is because the GAL essentially acts as a directory, and for very large companies, it could get out of hand to download all entries to a mobile device.
I hope this helps clarify! Are you able to find GAL entries when doing a search in your Android contacts?