Ok, so I don't need to sync it regularly then? It will do so every day, automatically?
Won't that be a problem for people with limited data plans? Doesn't Bitcoin Wallet need to download all transactions to find which ones are relevant to my wallet?
It synchs regularly, interval based on how long you did not use the app. It also triggers a synch when you plug in a a charger, which in many cases means you're also on WLAN.
If you don't send or receive coins, it basically just synchs the headers (12 kB per day plus some overhead). Plus transactions, if you have any (~500 bytes per tx).
If that's harmful to your data plan, you better disable mobile data entirely.