I was running firefox and seamonkey on my zaurus a few years back, so yes, a full browser can run on a mobile device. However fennec is not a "full" browser. The most useful feature of firefox is noscript - unfortunately the version of noscript for fennec is, for whatever reason, a severely cut-down version of the "desktop" one (no on the fly enable/disable scripts per site makes it marginally useful).

Mobile cpu/mem/power will always be a few years behind desktop so if mozilla codes for fennec in the same bloated way as they code for firefox then they will never "catchup". I think the mozilla have lost their way lately as firefox is seemingly getting more and more bloated and definitely slower whereas opera is still lean and mean.