No, GEOS C API does not provide access to the Noder features.
The C++ interface should not be used directly; the geos project views
it as a bug for another program to use the C++ interface or even to
directly link against the C++ library.
This warning is mainly for those users who rely on GEOS from packaged binaries.
This warning is to help avoid problems like those recently encountered by OSM projects, see osm2pgsql and libosmium.
Please, read also through the geos-devel list thread status of C++ API - is it a bug to use it or not?.
However, if you are control build process of your software and instead of relying on packages with GEOS binaries (eg. from your Linux distribution packages), and you can build GEOS yourself, then you will be fine.
Typically, breaking changes in C++ API are not very extensive, so it should not be a huge task or hassle to update your own source to adjust to the changes.
I have used GEOS C++ API in such way for decade, in large projects too.