We may have drifted away from the original question, which was whether 'patch through' can be used to mean 'make a (distant or third-party) telephone connection,' and if so, whether it would be useful to add that to LEO, and if so, how it should be translated.
IMO the dictionary definitions and Peter's and oreg's comments all refer to an *older* sense that emphasizes the temporary, inferior, manual, etc. nature of the connection. That is *also* a meaning that should probably be considered for LEO, if someone would just propose a translation.
However, the *other* sense, which David has already accurately described and documented, and which I further confirmed with still more web examples (bullet points above), is, again, not necessarily temporary, inferior, or manual at all. The U.S. Capitol switchboard, for example, can surely be presumed to use modern telephone technology to transfer a call to an office in another building. So can answering services that patch callers through to an on-call staff member's home number.
For me the distinctive feature of this sense is, again, the third-party connection. Indeed, it sometimes overlaps with 'put through,' but more often it has a narrower ranger of meaning that does not normally include just buzzing another in-house extension. You could say that 'patch through' is a subset or a special case of 'put through.'
Perhaps someone may yet offer a better translation than 'durchstellen,' 'verbinden,' etc. But in the meantime, surely there's no question that the term exists, that LEO users like ö encounter it, and that these are at least acceptable translations. So, once again, why not just go ahead and add it?
PS re 'richness of language and multiplicity of human beings' -- is that like 'life's rich pageant' in the painful sense? *g* related discussion:Life's rich pageant