As far as I can tell, Bash source code doesn't differentiate between
SYS_BASHRC and other included rc files after compilation. In addition,
SYS_BASHRC could be undefined, and the resulting binary wouldn't use a system rc at all.
All the files used by a process can be found out by
strace, however. Bash includes rc files only if it is run interactively, so:
echo | strace -e openat -o tmp.log bash -i 2>/dev/null
The resulting file
tmp.log will contain the information wanted:
openat(AT_FDCWD, "/etc/bash.bashrc", O_RDONLY) = 3
Unfortunately, it will also contain large numbers of lines e.g. for libraries (and the redirection to /dev/null). I'm not sure how to select the correct line in every case. But in practice I think it will most probably be the first non-library in
grep -v O_CLOEXEC tmp.log | grep \"/etc | head -n 1 | sed -e 's/.*"\(.*\)".*/\1/'