Bombay and some other places started out as British territory leased to John Company.I also doubt John Company is capable of self-sufficiency until the late 1700s.
As for some sort of civil war,I'd presume one side would generally lose quickly.In these kinds of civil wars,people tend not to try and fight to the death.They more or less try to flee or defect whenever one side seem to be losing,especially since the sepoys don't really have much loyalty to the British crown.
I would argue that the Company was self sufficient. Shame I don't have internet at home where my sources are :/
Anyway, most of the profits until the XIXth century were mostly in the country trade, which would not disappear with independance. The really big point is whether they can renew their armement and replenish their arsenals.
If we plan on the period 1750-1800, the attitudwe of France is key. Would they ally with the Company and fight Britain? Would they be neutral? Would they fight a three way war?
aht would really be the defining factor. If Britain can't have free access to a well entrenched Company, the bid for independance can succeed.
If Britain has access AND has backed for France, the bid is useless and will be crushed
If the Company is allied to France, providing them with gunpowder and a place in their European networks, now that'd be interesting as we would see a lot of the profits and networks that went to London go to Bordeaux or Nantes instead since Amsterdam had been crushed as a safe place to invest money