If the hot conductor was connected to the neutral terminal, and the neutral conductor was connected to the hot terminal, wouldn't every outlet in the house have reversed polarity?
It's AC, so 'reversed polarity' is of limited meaning. The 'neutral' (white) wiring in the house is still bonded and/or grounded at the service, so that's still your grounded conductor for testing purposes inside the house, and the only thing that really changes is the voltages.
Let's assume that any earth conductance back to the utility's grounding of the neutral is negligible; ( i.e. let's leave aside any shock hazards to actual 'earth' rather than to EGCs and bonded metal.) . And let's say that before the swap the neutral was properly bonded to the EGCs at the service. And let's specify that it was L1 (black) and neutral that were swapped, but we'll continue to refer to L1, L2 and N as they are labeled in the house. What you get then within the house is 120V between the L1 and N, 240V between L2 and N, and 120V between L1 and L2. And N is still bonded to EGCs, and thus still no voltage between N and G.
Therefore testing with one of those simple three-prong outlet testers would give the following results:
On receptacles connected to L1, the tester reads like it would before.
On receptacles connected to L2, the tester LED circuits receive 240V and will thus be either twice as bright as normal or burn up. But otherwise the light patterns still as before.
Also, If that's the case, a majority of the current would be traveling back to the transformer via the low impedance conductor, but a trickle will also be traveling back via the ground. (Electricity takes all paths of resistance).
This is true anyway if the conductors aren't swapped. If they are swapped, the difference would only be seen if the ground path is of sufficiently low impedance then it will essentially create a short back to grounding connection at the utility transformer. That should trip the house main breaker.
Also, a single ground to neutral short anywhere in the building, would cause some current on lots of bonded metal parts. Unless I'm thinking of this wrong. Check the outlets with an outlet tester for polarity swap.
No, it wouldn't carry any more current than such a fault would normally cause. Because in both cases it's the same parallel path between the the fault and the MBJ at the service. (The only caveat is that if the fault is on a 120V circuit that is swapped to see 240V, the path would be carrying roughly twice as much current if the load didn't fry open.)