Sorry for digging 2 years old thread, but I am not 100% sure to @hauleth post, which ended this discussion. Are we sure it cannot be run entirely offline?
At the time of writing the homepage https://www.tabnine.com/ has info regarding privacy & protection:
All of Tabnine’s code completion AI can be run locally on your machine. Your team’s code and AI training data are NEVER shared, helping to ensure your code stays compliant
and also:
Tabnine will NEVER share your code or use it as part of its open-source AI
and also going deeper, seems like sending code to their servers is optional cloud feature:
In case of not meeting system requirements (4 cores, 8 GB memory) cloud feature is the only way to run TabNine. I got message regarding not meeting requirements:
Your current setup doesn’t meet Tabnine’s local deep completion model requirements, so you can’t run Tabnine locally.
…
Don’t worry! You can still enjoy Tabnine’s deep completions using our cloud - it’s free!
And… requires Signing In/Up 
So it seems like, if you meet system requirements and you don’t sign up, you are in offline mode.
Further research could be done through monitoring network traffic, I haven’t done that.
