I must note, that reproducing this issue will require to disconnect your router from internet.
Lets say that device A is Android phone and B is Windows editor, both are connected to router via Wi Fi, router itself is disconnected from internet.

1. Download user attached project.
2. Disconnect your router from internet.
3. Reconnect device A internet connection
3. Open user attached project
4. Build & deploy to device A;
5. Play scene in editor on device B;
6. Use device B as server; click on "Server" button
7. In device A enter device B local ip address (I.E. 192.168.0.105); click "Client" button;

Notice that Network transport will now report that Connection was successful, but sending messages will fail. This does not happen when router is connected to internet.

Note: When connecting to a Wireless network without internet connection on Android device it will report that it's IP address is unavailable.
Note2: Device's has to be disconnected from internet before launching build/editor/etc.
Note3: User also reported that same scenario happens between to Desktop clients, when one of them has public firewall settings applied to it's connection - NetworkTransport reports that Connection is successful, but message delivery fails.

Reproduced with: 5.3.5f1, 5.4.0f3, 5.5.0b5