Does this work?
Can my students actually learn with this program?
Yes, they can learn. They can learn a fair amount of vocabulary (1500 words plus or minus a couple hundred). They will learn the verb tenses, articles, pronouns, adjective placement, and other basic grammar.
They'll need to use other resources for listening comprehension and especially for speaking.
The most important thing is whether or not your students apply themselves. We see a lot of students goofing off in the forums, posting nonsense or even rude comments, repeating "Basics 1" over and over to earn points and fool their teacher, stuff like that.
Duolingo is a good arrow in your quiver, but it's not the entire quiver.
Well, I started Danish from scratch on here, and jeg kan nu læse dansk. At least a little anyway. I've certainly learned something the last couple months, and that's with no outside instruction.