Writing with an online concordance has its advantages in terms of ready resources for students to rely on. It can be a time-saving device, and once 'hooked' on the system and the real-time answers to vocabulary or grammar questions, I can see how students would not mind writing in this manner. BUT the online sessions should be timed periodically throughout a semester for both the students' and instructors' sakes. Having the actual documents posted on one site for the instructor eliminates the awkwardness of e-mailing documents, which I cannot tolerate myself, when faced with exorbitant amounts of students. The drawback is the learning curve for familiarizing oneself with the technology.
Luxtutor is amazingly academic, however, which is its strength. It's a maze of resources, best used for the advanced, or EAP writers. Just becoming familiar and even expert at navigating the concordance would be useful in the students' future academic writing. I'm smitten with this feature: concordance of both written and spoken language! The bonus for me, also a French instructor, is that Luxtutor has both English and French concordances. BINGO!
