I did it partially while I was working on one for university. It works well enough, but obviously you will be rather slow because the software keyboard can't compete with a proper PC keyboard. I'd usually write for half an hour or so when I was riding the train but the majority of the work was done on the PC.
It also has got enough basic formatting options so that one can get the "look" right for the most part, but I did end up using Office on PC to polish it properly. I guess if your university is giving you a template to use and it's in the correct format (.docx is a must!) in theory you could write the whole paper using your phone.