Yes, writing at The Second City. The Second City Training Center is in the comedy-instruction business, and writing sketches, screenplays, and TV scripts is part of the comedy business. There's a market, and a reservoir of expertise, so they teach it. 
 
Second, the resident (mainstage and e.t.c) and touring shows at The Second City are at least 80% scripted, formally or informally. Pure improv fails about half the time. If you're good. If you're an improv aficionado, even the failures are interesting, but most of the audience wants to see a show that is reliably funny. It is no small achievement to be reliably funny; it is in fact a good and honorable thing. The Second City process for developing revues uses improvisational skills to develop scenes that will make up a good show. 
 
In some few cases, a scene will start as a script; trial and rehearsal will change it considerably. In most, a scene will be born in improv before a live audience (or in rehearsal), and go through the same process of refinement (possibly beyond recognition). The goal is to preserve the authenticity of sentiment and character that come of good, pure improv, but shave out the irregularities and dead spots, and enhance the scene's relation to the theme of the revue.  
 
So writing, even if by a group process, goes on all the time in the preparation for sketch comedy shows like the Second City mainstage. That's not a bad thing, and is worth learning.