The way it should work: Spine needs an internet connection the first time it is run in order to download the latest update. After that, it doesn't need an internet connection to run again.
There is a problem where users report that Spine downloads a new update every time it starts. Unfortunately, this is hard for us to fix as we have not been able to reproduce the problem, despite trying it on many different computers. If this same problem is happening to you, it could be that Spine thinks its update is invalid and that it must download an update. In that case if you don't have an internet, Spine fails to start because it thinks it doesn't have a valid update.
Can you post your Spine log? Are you running Spine in a virtual machine?