I check AE on my mobile phone every now and then (while having breakfast or while I'm not at home). It is really annoying having to zoom in and out to click every button (it loads the desktop version of the website), but you get slightly used to it. It's good if you need to quickly check your airline, maybe lower fares because of competition or add a few routes. But it is still much, much better to use a computer because of the mouse.
The other issue apart from having to zoom in/out constantly is when you open multiple tabs it's really hard to manage them. For example, sometimes I open tabs with the details of each of my idling aircraft to see their ranges, then another tab with "browse airports", and then some other tabs where I research the routes. It is already kinda messy in a computer (I wish I could see the info of each plane while adding the route, getting rid of most of the clutter) but the cellphone makes it worse because it's much harder to change between tabs.
So, it would be cool if we could get a mobile version of the website that is not cluttered and has easier to tap buttons. Maybe it would require getting rid of some info on some pages or putting it somewhere else though
Still, it is possible to use AE on a cellphone as-is for quick checks, but I wouldn't recommend it for more complicated tasks (setting up IFS for example)