Speaking as a non expert but having messed around with the electrics on my Disco 3 & Disco 4, incl fitting second batteries, have a little experience in this area. Would only work if the socket not “protected” by a relay. If the socket is permanently live then it doesn’t have a relay in there so is not looking for the voltage from the crank battery via the ignition key. Then a trickle charger would add volts to the system, enough to power up the locks. If it is protected, and the battery is dead, then the voltage it’s looking for will prob be too low, socket will not connect to the battery and the rest of the car.
Now talking of aux sockets, isn’t the boot socket, beside the little torch, perm live? That might be a route to get a trickle charger in though to give enough volts to open the locks. Bit of a clamber from the driver’s seat but not impossible.
Another route the LR owners use is via towing electrics, specifically the permanently live feed for the caravan fridges. They even have has specific adapters made to connect a C-tek charger to the main battery as a routine way of charging. Works well as long as peeps remember to disconnect before driving off.
PS This is the jumper cable arrangement used to make a socket, or series of sockets, perm live off the crank battery. No idea how it would look on a Karoq but the principle would be the same.
Re batteries sitting dead for long stretches after manufacture, my car was built late July 19, but not picked up by me until June 20. After 5 months and 4,100 miles it hasn’t missed a beat. It was a Skoda UK preregistered car, wonder if it was charged during that time or the battery was changed as part of the PDI process.