Using Mootools Element.Dimensions I can get the computed size, in pixels, of any element. However, I can find no way of telling whether an element has been sized using pixel
I doubt it can be done. You described the reason quite accurately: We have access to this kind of information only if it is in the element's style attribute. The only way I can think of is enlarge the parent container a bit and see if the textarea grows proportionately in size, but this is probably not always feasible, and probably hard to make cross-browser functional.
I'd be highly interested in more positive answers, though.