To answer myself (and future users, possibly):
Yes, you should worry. Not about iCor, but about the “internally” “installed” external tools. As @PM29 points out in their How-to-Sen2Cor notes, the “installation” via Plugins -> Available Plugins only installs a small plugin, not the tools themselves.
Became obvious when trying to run Sen2cor from within SNAP. SNAP noted that the bundled binaries need to be installed first and, nice, opened the corresponding window automatically and had that filled in properly already. Installed. Ran. Fine. Now Sen2Cor has a green hook. 
Not sure, whether the fill-in is always done automatically. That would be great. Or whether that had to do with that I had installed the stand-alone Sen2Cor already separately.
No time for now to check out and fix the remaining “internally” installed plugins/tools (Orfeo, Sen2Three,…). Might come back to that later.
In any case, I think, some notice in the installation notes on Sentinel toolbox/Third party tools webpages would be justified about that the plugin-installation is just… a plugin, it alone won’t make the user able to run the external tools. (on the other hand, if I understand correctly, one HAS to install the plugins. Which, as far as I remember, is not mentioned either in the third party tools intro or the external tool installation guides).