Hello,
I know it's unusual to answer his own questions ;-) However I in a different forum I was quickly pointed towards the answer:
SAP Note 1835958 from 2015-07-28:
CBTA 3.0 : Known Issues
[...]
6. Limitations related to the Browser
[...]
NetWeaver business Client (NWBC) is not supported.
[...]
Original document:
http://service.sap.com/sap/support/notes/1835958
(SAP marketplace login required)
Naturally, this brings up the follow-up question: now is there an SAP tool for testing NWBC? And if not, is there a recommended 3rd party tool? As these questions aren't covered by the thread's headline, I will start a new one.