Short roping is a technique that is mainly used by mountain guides to get people up a mountain without the need for a time consuming proper belay. The whole concept of short roping is not to catch a fall but to avoid a stumble escalating into a fall. As such short roping is a dangerous technique because only "under ideal circumstances it is possible to hold a fall on a 30° slope" (Source, unfortunately only in german: http://www.bergundsteigen.at/file.php/archiv/2008/2/print/54-61%20%28verbunden%20bis%20in%20den%20tod%29.pdf )
Therefore the use of short roping is heavily disputed due to high risk. The german alpine club completely discourages it while the swiss alpine club encourages the use mainly for psychological factors and being already tied into the rope when you reach a section that requires a proper belay again (instead of heaving the rope in your backpack and continue ropeless).
Given this background, your fear is completely rational. There is a substatial amount of guided groups with too many (I have seen up to 4) guests at a short rope which also have a bad technique and are therefore very likely to stumble and fall. I would not join such a group.
However, there is a difference between a guided tour (which intends to bring you on the mountain and back down again safely) and a course which is intended to teach you the necessary techniques to go mountaineering yourself. If there is a substantial amount of short roping in a course, it is no longer teaching. Moreover, most of the teaching does not require to go into terrain where short roping makes sense as it would then be too difficult.
So this mainly boils down to find a good course. Before booking you can ask about short roping and also about all the other contents of the course. This will also help to align the course with your background. If you already have experience with alpine rock climbing, you will need a different course than not having any related experience at all.