It happens that pinnerite formulated :
The radiatprs are c 1968-70. Assuming that electrolytic action has
hollowed them out and that they may need replacing, are the copper pipes
likely to be equally affected?

Copper, no, however.... Radiators rust from the inside out, if they
have not been kept topped up with inhibitor. The rust and gundge tends
to then block copper pipes, especially so the small bore systems.

All depends on how well the system has been looked after.