Sorta but not really. If you model the grid as a superconductor, sure, but the transmission lines we use do have resistance and therefore a maximum capacity and the father from generation you are, the more losses are incurred to get the power to you. So you end up actually getting power from the generating capacity close to you and occasionally get power from further away (or your local generation sends excess further than normal).
If you have 2 buckets connected at the bottom by a small hose, and you take from the left bucket at a high enough rate, the buckets will be at an unequal level and at some point either you stop taking and the water eventually seeks its own level again or your take rate becomes that of the connecting hose. (this extension of your bucket analogy, like all water/electricity analogies, breaks in a lot of ways but it gets the idea across at least).
But not really; if your local regional plant is nuclear and is consistently the contributor to the lesser sized coal plant in the next region, then the emissions for your bev are less than the coal region.
And given how often Nuclear does provide greater base load than smaller coal plants; if your most local plant is nuclear, your emissions are less.
Yes and no. It's a shared grid (except most of Texas) but for the most part your power is still coming from local sources. The sharing is to balance out extremes, not for constantly moving power from Vermont to Georgia. That would be extremely inefficient.
In addition to location mattering as others have pointed out, time also matters a lot. Charge up during the day, you might be using solar. At night, that isn't likely anymore.
It’s not a shared market, only a shared grid—through the magic of accounting, you can purchase renewable energy even if the actual electrons came from a fossil fuel plant.