Mark wrote:

If you just connect a normal socket to the same terminals the existing
socket is being supplied with, it will not be protected.

Why not? Isn't the RCD measuring earth leakage irrespective as to
whether something is plugged in 'in front of it' or 'behind it'?

To give you the simple answer you obviously want, then No!

Years ago, voltage-activated ELCBs were sometimes used. In some cases,
these might have triggered owing to a fault current in the way you
describe (but not to an extent you'd want to rely on).

Today though, we use RCCDs that work by detecting currents and they
will only do it for "downstream" devices.