I'm glad you were able to make it home safely. I did the same thing with my 1988 Accord in law school many years ago: filled at a gas station off their garden hose. For other owners, I would not recommend doing that with the NSX. Ever. The water pump flows 150L of coolant per minute at 6,000 rpm, or 2.5L per second. That means the water pump will empty the entire cooling system (16L) in about
6.4 seconds. You get a few more seconds at slower engine speeds, or with a smaller rupture (like on the heater or oil cooler lines). Adding a gallon of water gets you about 2 or 3 seconds of driving before the system is dry again. Even worse, all the air that gets sucked into the system must be purged before you can run the engine again, or you risk steam bubbles at the deck surface (air rises) that will destroy the head gasket and warp the heads. This happened to me at the 2012 NSXPO track event (heads were ok but gaskets were trashed), and that was with a fully filled coolant system letting in air.
When a big hose fails, the best thing to do is shut the car down and don't run it again until you have repaired the hose, filled the coolant and performed the complete bleed procedure to purge any air. Then, you should do the compression test and block gas test to make sure the head gaskets are intact. Your block gas fluid should look like this:
View attachment 184989
If it turns yellow, you must replace the head gaskets and likely have your heads milled.