Graphic design, for print/publication. Presumably using InDesign/Quark...
It's not drawing by a long shot, but it can be fun if you're into typography and playing with shapes to best fit the content. I've worked and am still doing bits and pieces of design work for the past few years; I enjoy it, and I like how it helps drawing and painting, but if you're not into laying out spreads or the like, it might not be for you.
What cotron said. In graphic design, you can choose between print and non-print design, the first being design for magazines, flyers, posters, books, everything related to printed paper and the second being web- and application design.
You basically don't draw alot, illustration is mostly done in vector-based programs or with photo-manipulation in Photoshop. I don't know what position it is exactly that you're looking at, but you will probably be making layout-design, meaning typography and pictures mixed on a page.
How long is the traineeship going to take? I spend the last 2 years doing that job in a traineeship and will be doing the finals in december. It's a cool job and if no better opportunity arises, I think it's solid. Always depends on how good your company is and how new their software is (the new software like InDesign and Illustrator really do alot of work for you, whereas Quark and Co. are buggy littles bitches, my opinion ).