As far as I know, you are only going to be able to do what you want if you are using the CH Control Manager software. In which case, yes, you can map a switch or hat press to the Enter key, or a string of keys, if you want.
I use the CH control manager software in part because the original sim I played supported only a single controller, and over the years, the very very few other games I've played generally worked better if I had more control than they gave me over the controller. AH does just about everything I've ever wanted through it's own interface, so I have devolved back to a pretty vanilla profile for use with it over time, and would likely be just fine without it, but I do like the fact that the control manager seems to eliminate all of the wierd calibration mismatches between Windows and AH.
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