Once you have learned the basic tai chi short form, you may try to practice at a higher speed, but it would be a while before this would feel comfortable and it would be hard to gain the full effect unless you were doing it correctly. Yes, the moves would become more apparant but not one hundred percent. I would suggest speaking to your instructor about what the applications of each move would be. I am sure you realize that it is hard to do tai chi very fast, but it is also very hard to do the form very slow.
Medium speed is what people do mostly.
Keep in mind also that the speed must also be measured in parts. The entire form should be evenly paced. Most people start out slow, and then speed up when there is a strike or retreat. Try to be consistent. If you intend to make this a part of your routine, I would do so sparingly, until you are extremely comfortable with a slow to medium speed.