As far as I can tell, Running Status is a function of the MPU-401 midi interface (and maybe also compatibles/clones ?) and was never anything to do with any other midi device, module or keyboard. Hence it is very possible that no devices of the type you refer to create data with RS, although keyboards may well recognise RS and allow for it.
I've not seen any reference to any sort of command that will make a midi interface (such as the MPU-401 type) turn RS on or off. I have a Roland Tech Ref Manual for the MPU-401 interface which has reference to RS, but no mention of any option to turn it on/off.
There may be many devices now that do not use any interface compatible with MPU, and therefore the use of RS may be redundant as hardware generated. RS may still be used, however, in midi files.
I'm not sure if it's relevant to your question, but I think that one of the problems with the Chinese USB/Midi adaptors that cause so many problems relates to RS - the interface often does NOT cope with RS correctly. When it received RS data (i.e. without the Status Byte) it seems to correctly add the status byte from the last complete command, but then corrupts the following data bytes. Upon receiving a complete message (incl Status Byte) things are reset and OK.
Are USB midi interfaces considered to be MPU-401 compliant?