There are numerous scientific & engineering articles published, instructions written, circuitry built to prevent and test, etc... -- all about "ESD" - Electrostatic Discharge in network electronics caused by CDE - Cable Discharge Events.
There is no point in linking them here: the interested people can easily google for "Cable discharge events ethernet".
Here is just a quick example - an
application report by Texas Instruments.
This might not be the best document to describe the safety procedures, but it is a good example indicating the vector(s) of the danger: discharge that happens when you
connect a network cable to the equipment, and explaining how that happens. Of a particular interest pertaining to this discussion is p.2, the bottom half in particular.
This article goes into a more detailed description of the CDE, and how it occurs, and the relevant parameters (such as voltage developed, time scale, etc.):
Unless its causes and cures are understood, electric-charge buildup on LAN cables can result in system failures.
www.electronicdesign.com
Of a particular interest to this discussion is this quote:
"Once charged, a high-grade cable can retain most of its charge for more than 24 hours."
So, disconnecting the cable for 10 minutes or even 1 hour may not discharge a cable.
tl;dr: Connecting an Ethernet cable to an Ethernet port can result in CDE.
To minimize the potential of a detrimental CDE, it is best if the person connecting the cable is grounded (and if the
cable itself is grounded prior to connection).
Obviously, if you can reduce the number of times you connect/disconnect the cable, you lower the probability of a CDE (especially since many (most?) DIY@home equipment installers (and even various ISP installers) do not ground themselves).
Those are evidence based facts.
Now, a speculation: Can a CDE have *some* positive effect? It is not totally impossible in case your equipment is already malfunctioning, say due to the damage caused by the previous CDE: by zapping a blown fuse you might be able to fuse it back by creating a narrow path.
But relying on that would be akin (for a medical doctor) subjecting to the first-aid electric shock all patients regardless of the reasons/problems they came with, even those who came for a physical check-up, - hoping that it will not kill them.