Dramatic illusion refers to an actor using the skills of illusion and acting to recreate either "actual or imagined life" (Encyclopedia Britannca, "Theatrical Production"). Bernard Beckerman gives the example of a tightrope walker. An acrobat who walks a tightrope is "performing an acrobatic act," but the actor who is pretending to be an acrobat and creating the illusion of walking a tightrope is creating a "dramatic illusion" ("Theatrical Production").
The mechanicals definitely use a great deal of dramatic illusions in their play. In fact, they have actors not only playing the roles of the characters, they even have actors playing the roles of animals and inanimate objects. Snug, the joiner, is assigned the role of playing the vicious lion that frightens off Thisbe, making Pyramus believe Thisbe has been eaten by the lion and leading to both Pyramus's and Thisbe's suicides. Snout is assigned to play the wall through which Thisbe and Pyramus whisper to each other. The wall costume is put together with plaster, and he holds his hand out with his fingers cupped to represent a chink in the wall. Finally, they even have Starveling play the part of moonshine. He walks onstage holding a lantern, a bush, and--for some reason--having a dog in tow.
However, for all their uses of dramatic illusion, it's very clear they have no real understanding of what dramatic illusion is. We know this due to the fact they feel inclined to explain to the audience what all of their illusions are. For example, Bottom and the others are so concerned the ladies in the audience will be offended by Pyramus's death scene that they feel obliged to write a prologue explaining that the death is not a real death; they also want to explain that the lion is not a real lion, as we see in Bottom's lines:
Write me a prologue, and let the prologue seem to say we will do no harm with our swords, and that Pyramus is not kill'd indeed. (III.i.15-17)
Since the mechanicals feel the need to explain their illusions, we know that they have absolutely no understanding of what dramatic illusion is and what purpose it serves. The intention of dramatic illusion is of course to make the audience believe in an illusion--believe that what is not real really is real.