The short answer is sort of yes, but not really, because it depends.
The first question is whether or not you are talking about a rechargeable battery. And is it a a deepcycle wetcell? Gelcell? Sealed?
If you are using a disposable, 12v 5 amp hour battery, then more or less, yes, 1 amp draw = about 5 hours power.
If you are using a rechargeable deepcycle wet cell, the answer is more complicated. A deep cycle should never be discharged more than about 50%, so already you are at only 2.5 amp hours of usage. And if you actually want the battery to last at anything near its rated number of discharge cycles, you really shouldnt discharge it than about 1/3. The rule of thumb for sizing battery banks for boats is: 4 times the anticipated maximum usage between charges.
If you are talking about a thin-plate cell like a car (or more likely, motorcycle) battery, you really don't wnat to draw that battery down much at all. They are not designed as deep-cycles, since once you start the battery the alternator immediately starts charging. They are designed for very short term high-current loads, like for driving the starter for your engine.
I can't however give you much insight on nicad type batteries. I'm not sure about the draw issues on those.
I just now realize that you may not have cared about any of this, and you might have just been asking if your understanding of the definition of amp-hours was correct... in which case, the answer is a simple YES! One amp hour = one amp drawn for one hour.
-nathan
