/etc/bashrc is not used to customise bash at startup, according to the GNU Bash Reference
which says that the only global (as opposed to personal) file used to customise bash at startup is /etc/profile and that only for login shells.
The login shell restriction seems not to matter regards setting $PATH in shells running in terminals started from the GUI; investigation shows they have the $PATH that is set in /etc/profile. ps -H -U$LOGNAME -o pid,longtname,start_time,command
output suggests that a graphical login does start a login shell so all shells running in terminals started from the GUI will inherit the environment variables set by that login shell including $PATH.
@vhn: it is common to source ~/.bashrc from /etc/profile. This ensures that login shells are customised in the same way as interactive non-login shells. If you want non-interactive non-login shells customised in the same way you can set environment variable $BASH_ENV in /etc/profile to ~/.bashrc. If you want bash, when started with name sh the startup file usage is different as described in the link above.