Yes and it is also important to point out that if this is true, there is even more reason to be careful with your life and health.
You would have a situation where your family experiences your death in one reality, but you might continue on disabled in another. It only requires you to be conscious, but your physical condition doesn’t matter beyond that.
I would imagine it could continue on until it absolutely can’t anymore. At which point it either ends, or some kind of ascension or rebirth.
Hopefully your soul, higher power, the universe, etc would have choice or mercy at some point. Maybe you eventually accomplish what you needed from this life.
If it is purely physics without choice then you would eventually find yourself as one of the world’s longest living people. It would keep branching until the very last reality where there are no more where you can possibly survive. At least you would have a good answer when people ask your secret to long life lol.