Full steps mode for Z axis stepper controller
Focussing on the questions at hand:


  Is it possible to use full steps?


This depends on your printer board. Many boards use dip switches to select the (micro) stepping mode of the stepper driver. E.g. a RUMBA board has dip switches located underneath the stepper driver boards (e.g. DRV8825 or A4988). Sometimes you also see jumper caps. The answer is both yes as is no as it depends on the board you are using.


  Does it improve accuracy if I use compatible layer height (like 0.04mm,
  0.08mm, 0.16mm, etc) for my printer with 0.04mm per full step on Z axis?


Increasing the number of microsteps results in reduced incremental torque (for full step this is 100%, for 16 micro steps this drops to about 10%; this implies that a micro step requested by the controller may not effectively lead to an actual step as it cannot overcome the torque to turn the shaft). So highly loaded steppers could result in positioning errors. Resolution increases but accuracy will actually suffer. Furthermore, Few, if any, stepper motors have a pure sinusoidal torque vs. shaft position and all have higher order harmonics that in fact distort the curve and affect accuracy. according to this source. On the other hand micro stepping makes rotation go smoother (major advantage, see source). Interesting literature (must read) is this test and this paper.  

The answer to this question also depends on the situation; when you load the steppers very highly, using micro stepping may result in more inaccurate movement compared to full stepping. When you use the lead screws native resolution for your setup, only when the stepper is actually at the full step position, you would benefit as in this position it will not dwell to the next full step as it is already in the stable position.



As a side remark I've added the correct calculation of the native resolution of your lead screws. From your question I deduce that you have Tr8x8(p2) lead screws. "Tr" for trapezoidal thread, followed by the nominal diameter in mm. The digit after the "x" tells you how much the nut advances per revolution, this is called the lead of the screw. The value between the brackets "p2" denotes the pitch. This means that the screw has 8 (lead)/2 (pitch) = 4 starts. So with every revolution of the stepper (200 steps) the nut advances 8 mm which translates to 8/200 = 0.04 mm per step of 1.8°.