Most newer phones with GPS will work in airplane mode UNLESS you have an iPhone. I could be wrong, but I think Apple disabled GPS in their airplane mode.
It could take longer for the GPS to locate you if you don't have mobile data. Like gfunkdave said, mobile data helps to speed up the process. It probably won't take that long with the newer chip.. maybe 10-15 seconds? Now if you completely turn off the phone when the plane took off.. it could take longer to get the lock after you are in the air. And you will need to see at least 4 sats.