This is why I said in the other thread
But you didn't ask for clarification there, so I just blab it out unasked:
That instruction donates a seperate thread to the system (where it can run or block) and your application can run unimpressed of any system blocking in its own thread.
That's why your blink code works with it, but the root cause for your problem (the inability to connect to the cloud) doesn't get solved by extra threads.
That's the reason why @BDub suggested to get the code running without SYSTEM_THREAD(ENABLED) first, since clearly we can get out codes (including the doc samples) running with and without SYSTEM_THREAD(ENABLED).
Maybe you reflash Tinker via
particle flash --usb tinker
Then get your Electron into breathing (not blinking) cyan (not any other color) and only after that try to move on.