No it doesn't but it is certainly susceptible to leakage in wet conditions which are very prevalent in Sevenoaks Tunnel in places.
The problems on the NLL were due to mixed traction as the OLE has the running rails solidly bonded back to the masts which isn't what you want to be doing with a DC railway. Various solutions were tried in an attempt to minimise leakage and the best for just to have it as AC of course.
It can do but the installation of Cathodic protection is employed on risky assets like gas and petroleum pipelines to mitigate against that although with plastic or plastic coated pipes the norm today its needed less.
It's a common misconception by NR that their 3rd rail doesn't leak that much. It's not helped by the fact that all the earth returns are joined up in some areas making accurate measurement impossible. Leakage levels around New Cross were so high, that the conversion of the ELL from 4 rail to 3rd rail required a section gap long enough for no unit to bridge the gap and relies on coasting. The ELL was built with modern return trips so if the current out didn't match the current back, it trips the power. We also used copper return mats between the tracks & metal pipes.
I worked on the NLL, I don't think that any earth return existed due to the bodge job conversion from 4 rail to 3rd rail. Leakage measurements were so high monitoring equipment got fried!
I did a lot of work around Catford and a few other areas measuring stray currents. Whatever the weather, you could see passing trains on pipelines measure a mile or more away. The graphs showed train time, load & train length from a remote monitor on a pipe.
Stray currents occur at all times. The rails are often embedded in the ballast and even the 3rd rail in places. I have some pictures I took of the ballast nearly at the top of the 3rd rail.
Cathodic protection? That's a laugh, so many fried by extreme current leakage!