Just to close this issue and probably help somebody else with similar questions in the future:
It seems that the Android SDK (which includes ADB) is not allowed for redistribution. Quoting from Android’s T&C:
“3.3 Except to the extent required by applicable third party licenses, you may not copy (except for backup purposes), modify, adapt, redistribute, decompile, reverse engineer, disassemble, or create derivative works of the SDK or any part of the SDK. Except to the extent required by applicable third party licenses, you may not load any part of the SDK onto a mobile handset or any other hardware device except a personal computer, combine any part of the SDK with other software, or distribute any software or device incorporating a part of the SDK.”