Which also leads me to think that there's no real reason to believe that this discrete episode of consciousness would have been continuous since birth. For all we know, we may die little deaths every time we go to sleep, hit our heads or go under anesthesia.
Well, I'm a materialist and I say yes. Materialism doesn't preclude the existence of information which can be represented by matter. Recreating matter in the same arrangement/configuration as before reproduces the information.
If I copy down an equation, is it now a different equation? Of course not. It consists of different material for sure, but it's the same equation.
The same goes for us living in a simulation. If there is only one universe and that universe is capable of simulating our universe, it follows we have a much higher probability of being within the simulation.