Naturally, if you say something like Lisa Lin is a model student, with the indefinite article, there is no reason to believe she is the only one; there are probably others. However, saying We have selected Lisa Lin as model student, with no article, makes it sound as though she has had some honor bestowed on her, or that she has been appointed to a named position of which there is only one. Now, there are no other model students; she is the one. In that type of context, omitting the article is appropriate. For example:We have selected Lisa Lin as model student.
We have selected Lisa Lin as hall monitor.
We have selected Lisa Lin as Homecoming Queen.
We have selected Lisa Lin as Governor of Taipei County.
...where in each case Lisa is the only one of those. You see what I mean? It's kind of like saying
We have selected Lisa Lin as Model Student 2009.
(There's only one, and she's it.)
It is in this sense that omitting the article is correct, and this is the type of meaning that the sentence conveys. Thus, if that's your meaning, fine. If there is only one student selected as Model Student and it's none other than Lisa Lin, fine. You might even consider capitalizing it, but you don't absolutely have to. That does, however, give it a bit more grandeur.
Hope this helps.