Given you can put your controller/phone into flight mode and still fly, then securely download any imagery or whatever from the memory card, and that you can download firmware updates for offline application as well, there's absolutely no need for a drone to ever be either directly online or connected to a device that is. There is a corner case where a foreign operative using something like Aeroscope might be able to eavesdrop on Drone-RC comms while a drone is in operation, but that would entail being within range (possibly extended via the use of a parabolic antenna) of the drone and/or RC.
I'm going to go with a "No" on your question, unless you are either A - incompetent, or B - routinely doing flights over sensitive locations that are within maybe 10km of adjacent publically accessible land. Both of those scenarios probably do apply to government agencies and their sub-contractors though, so while for most of us this should be a non-issue, it's definitely a valid concern to a small number of operators.