Some good, concise definitons of class A operation have be posted to this thread. From my perspective, as a listener not an engineer, there are some other things to consider about class A amps.
One is that, while they are theoretically optimized for maximum sound quality, they run very inefficiently since the output circuitry is always on and is prevented from switching. For a power amp that you would use with a larger stereo system this means the amp will usually run very hot and need to be properly ventilated as such. In a portable amp, I suspect they too would run a bit warmer although I don't know if the small size of the componentry makes them feel any warmer to the touch. What you will notice in an amp like the Portaphile, which runs on batteries, is that when run as class A I suspect the battery life would be shorter than what it currently is. That would be a trade off in convenience versus sound quality to consider.
The other thing I have found, from experience with power amps, is that class A operation does not necessarily translate to better sound quality. I have an old 45 watt per channel amp that runs class A and its a great sounding product. I also have a 200 watt per channel Aragon 4004 which I believe runs as class AB. Most amps at that high a power rating don't run class A. Nevertheless, it remains a fine sounding amp. The class of operation is something that you really can't easily hear. Most of the amps on the market fall into the AB class which, with proper design, means they operate class A over most listening situations and fall back to a slightly less
pristine mode of operation when stressed.
In any case, if I owned a Portaphile and a class A upgrade were offered to me I would probably go for it.