I think there's a ton of misunderstanding going on, so let me chime in (I took a few classes and wrote papers on wireless networks, so I might know a few things):
1) I've read online that Airdrop does indeed require devices to be on the same local wireless local area network (WLAN.) However, if you're using two machines that aren't tied to a wireless network (for example, two iMacs that have wired Ethernet for outbound internet access, so their WiFi cards are free), they can turn on their wireless cards and establish a temporary ad hoc network for file transfer. However, if the two devices already have an established WiFi network that they use, chances are they have to be on the same network for Airdrop.
2) In the context of WiFi, I have never ever heard of a single wireless radio connecting to two different networks. Assuming you have one of the newer wireless cards that uses multiple antennas (this is called a MIMO system if you want to Google it), it's possible technically but still seems highly unlikely.
3) For those of you who say ad hoc mode isn't technically a network, it is. Any time computers communicate over a medium, whether it be copper wire or radio waves in the air, it's a network. "Ad hoc" just means no single wireless access point (AP) is required to negotiate communication between devices. The devices themselves directly negotiate the terms of communication without any AP present within the network.