Your impression is incorrect. If done correctly the cable can be used to engage or disengage the overdrive while moving. When you start out from a dead stop with the overdrive cable pushed in you are in direct drive until you reach sufficient speed for the overdrive to engage.
As mentioned previously the general practice is to leave the system engaged except for towing or driving down mountain roads.
There is a massive amount of information on this site regarding the operation of overdrive transmissions. Ford, Studebaker, Hudson, Rambler and other sites have similar data as they used overdrives for many years.
You can also find this information in the shop manuals and vehicle operation booklets.
Properly wired and operated overdrive transmissions will perform well for many years trouble free.
Fred
Last edited by rfs56trk; 05/07/2016 4:25 PM.