Not necessarily. Depends on where the problem is.
Doesn't even have to be on the same circuit, a link between N-E somewhere else could cause it to trip, but whether it does would depend on the loadings of the other circuits and how much current flows between the various interconnected parts.
It's a TN-C-S arrangement so there are all kinds of ridiculous current flow possibilities.
These heaters also have 2 separate circuits to them, with 2 separate CPCs to 2 separate consumer units, so that will add even more possibilities for current to be shared between various conductors in complex ways.