No, you don't need the second breather. I ran my 1937 RH for many years and miles with only the breather on the back of the case with no problems.
36 4G, 37 VH, 53 ex ISDT KHA (project), 54 KH(A), Healey 1000/4 (project)
Former Machine Registrar & Archivist, General Secretary and Single Spares Organiser (over a 25 year period).
Now Archivist once more - but not Machine Registrar.