The idea is brilliant I suppose,
the major skill non-native learners have problems with is writing. I teach writing classes and I find utilizing various techniques helpful. Your idea is cool and would be even enhanced if particular considerations are also involved.
In my idea, it's not a good idea to thoroughly ignore students's accuracy. You could make use of moderate feedback on form to correct the grammatical, spelling and any other possible errors students make.
One major issue with writing, is L1 interference. Students directly translate their L1 into English and the results sometimes are ambiguous sentences that might be grammatical but are not natural English and natives or readers in general might not understand them. So this needs a lot of exposure to the "right" language and of course, teacher feedback.
The idea can be even more inviting if there was some sort of competition between the groups and the group with more "likes" for example gets to win something interesting, like discounts with next term registration for instance if institutional policies allow.
Thank you for sharing your idea. and please keep us posted with the results of the activity.