Story points are designed to compare baskets of varying sized stories
...should we expect that we could approximately four 2-point stories completed in the same time as an 8-point? or thirteen 1-point stories in the same time as a 13-point story etc?
Yes, but stretch don't stretch it to the extremes.
Use that equivalence at the sprint velocity level. That is what is the very purpose of story points. You are trying to make a rough assessment of how much you can schedule into each sprint with a reasonable chance of completion.
However, two cautions:
But that does not mean you should say something like, “One story point = eight hours.” Two developers can start by estimating a given user story as one point even though their skill level may be very different.
Don't use story points for Sprint Planning. During sprint planning break-up product backlog items into tasks and estimate each in hours. This will give you a better handle on how much the team can committ.