If it is a proper heater, it should not take long to heat up the water... my 50 Watt heats up my 5 Gallon and stabilizes after about 30 minutes? Maybe even less, I don't really notice because I float the cup in there anyway to keep Bobo warm during water changes.
If it is underpowered, it would take a very long time and it may be very unstable...dropping in temperature every few hours because the heater cannot handle it. It also might damage the heater
I don't have any predictions on overpowered heaters, but my guess would be also wildly fluctuating temperatures and damage to the heater constantly going on/off/on/off just to heat up a little bit of water. It also may or may not turn on because the thermostat is not as sensitive as the smaller heaters, causing fluctuations again.
I'm not really sure what to say...it's either risking your fish or breaking your heater :(
Okay I just saw your post lol... I would say it shouldn't take too long to heat up the 1 Gal...I'd give it maximum 2 hours on the safe side. Just check it constantly to see how fast it takes to heat it up a few degrees. If it takes literally a few seconds to bump it up something like 4 degrees, then it is probably overheating >_<