Yes this will work, you just have to see if the high pressure side of your regulators is left or right hand thread. Some are right hand, some are left, so you will need to buy the appropriate pipe nipple.
This store has a right to left hand thread adapter. Right-right and left-left should be available at a hardware store or Mcmaster.
You also want to make sure that they are both 'primary' regulators so that they have the correct diaphragm for regulating tank pressure. 'Primary' regulators have a CGA-320 thread on the inlet, 'secondary' regulators have a hose barb on the inlet.
This is what my setup used to look like before I realized that you cannot connect a 'secondary' regulator directly to the gas:
