The idea was originally patented by William Hurlock and AC (Acedes) Cars in 1936/37. The patent number is GB470786A - Auxiliary Silencers. Details of the patent can be found through the UK Patent Office search engine espacenet.
I imagine the boxes helped damp out noisy resonant frequencies. Whether the theory outlined in the patent would stand up to scrutiny against the current understanding of resonance in exhaust systems is doubtful.
As the boxes are branches off the exhaust system, rather than through boxes, it seems unlikely they would cause any resistance in the system. However, resonance in both intake and exhaust systems can aid, or hinder, the fluid flow rates. The impact these boxes have in that respect are not known to me.
In the 1950s, on our family Two-Litre, my father replaced the two auxiliary silencers with smaller diameter tubes of the same length as the originals. I can't recall if it made any difference but the replacement items were made of power station boiler tubing and lasted much longer!!
I have a vague recollection of replacements being made to original drawings about 15 years ago. Brian Eacott may be able to help.