Not addressing any potential legal issues, airline security related stuff, contractual agreements, or terms of service issues but from a strictly technical stand-point yes.
Almost all of the airlines allow the use of their own apps or connections to a given airlines home page without paying for the service. In order for that to work they allow people to connect to the 802.11 network prior to payment/agreement of terms. Therefore yes you will see some traffic including the access point's mac address/IP address and some of the traffic on-board. There is nothing really unusual here in that it's just a normal 802.11 network using your regular built-in 802.11 wireless device drivers and you will see 802.11 traffic as you would anywhere else.
This said I think you'd learn more from downloading a lot of sample PCAP's of varying protocols from WireShark Sample Captures page:
https://wiki.wireshark.org/SampleCaptures
Hope this helps.