Yes, “airplane mode” disables all methods through which the device voluntarily transmits information over wireless networks. That's the point.
The device is still emitting, of course. For example it emits visible light: all information that is displayed on the screen can be snooped by shoulder surfing or hidden cameras.
Even information that is not voluntarily emitted can sometimes be snooped. Whenever a variable current is sent over a wire, this creates an electromagnetic field; in principle, extremely precise measurements could reconstruct the data traveling on each wire. In practice, this kind of snooping is fairly easy for CRT displays (which emit a lot of radiation) and requires mildly expensive equipment for LCD. For anything smaller, it is all but impossible to discriminate between the many buses, or at least far more expensive than hiring a goon with a monkey wrench. This still leaves radiation as a side channel, but to exploit it, you really have to know what you're looking for.
For all practical purposes, a device in airplane mode used in a situation where no shoulder surfing is possible is immune to eavesdropping.
Note that if malware is present on the device, all bets are off. Malware could pretend that the device is in airplane mode when it isn't, or more simply, record data to send later.