I get asked this from time to time. The simple answer is yes you can but just be aware of a couple of things.
If you opt for a class where the judge may ride, do not be offended if they decline. In the showing world, tradition is for a treed saddle, if showing if your chosen sport you might like to get one. 🙂
You may be marked down for being in a treeless in the show ring in a less than traditional looking model. Some judges just do not like them. If you want something traditional looking go for a Solution.
BD rules state that you can use a treeless saddle providing it is of a standard design, ie not western looking. If you want something traditional looking go for the Freeform, Barefoot or Sensation Dressage models.
We have had success in the Freeform Classic though. 🙂