I don't think there's much of a question as to how connected the universe is. I may be misinterpreting what you meant, but this is how it seems.
I'm sure the entire universe could be represented as a giant cubical grid X-Y-Z coordinate system as long as you define the X, Y, and Z axes (which will be fairly arbitrary, like defining the X-axis as the line from the Sun to Earth). And, given this coordinate system, I could measure with confidence the distance between any two points no matter how far away or what is in the middle simply using the pythagorean theorem. Since the universe itself likely isn't cubical, some of the grid points would be undefined, but its just an arbitrary reference system... you could do the same with polar coordinates or anything else.
However, such a system would be rather pointless, just as developing a single unified X-Y-Z coordinate system for Earth would be pointless. It could be done, but having local datums and northings/eastings are easier for us to work with, and lat/long/bearings are easier for us to navigate. Hell, even the shortest path between two points on a map is an arc rather than a straight line, so its better just to come up with local systems that work for us.
Nonetheless, you could make an arbitrary coordinate system that applies to the entire universe and be certain that all spatial relationships within your established coordinate system will remain intact. The calculated distance from A to B would be the same as if you laid out a giant inflexible scale between A to B in the physical universe (assuming no material deflection, stuff in the way, etc). It would be a meaningless number, since it likely won't be the path of least resistance from A to B, but the spatial relationships will hold.
Afterall, you're in the universe right now. Point A is connected to Point B in the way you expect it to be, and there's no sudden jumps or elongations or compressions involved in the travel from one point to another due to the nature of (disconnected) dimensional space itself. Phenomena in space may cause some distortion, or even apparent elongation and compression due to relativistic scenarios, but I doubt space is disconnected in such a way that there is a location in the universe where moving a meter will actually move you twenty (in any single arbitrary coordinate system that includes both your origin and destination).
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