Is disabling all the wireless connections the same as enabling "airplane mode"? I'm confused right now because I don't know if enabling the airplane mode disables all the data connections or it does something more.
I didn't dig into the source code for authenticity so consider this as an educated guess. I noted that when turning on Airplane mode only the radios mentioned in the key airplane_mode_radios1 are turned off. That is, the communication through those radios cease to exist. The list of radios in the value for that key I've seen in my devices are: cell,bluetooth,wifi,nfc,wimax,

where, 


cell: cellular radio (used for mobile network connectivity)
bluetooth: used for bluetooth connectivity
wifi: used for Wi-Fi and portable hotspot connectivity
nfc: for NFC
wimax: ??


So yes, if you individually disable all the radios listed in the said key in your device then you would effectively be achieving the final result of Airplane mode.



If it matters, I found the value for the said key using adb through the command: 

adb shell settings get global airplane_mode_radios




1 The key can be found in the table global of database /data/data/com.android.providers.settings/databases/settings.db. In Android 6.x, the location for the key is /data/system/users/0/settings_global.xml