Duplex mode 3 might be used with a repeater where in-cabinet repeat cannot be disabled. It has the advantage of no audio delay introduced from app_rpt. However, the disadvantage is reduced repeater control: time out timer, Tx on/off, CTCSS on/off and repeat audio level adjustment must be provided external to app_rpt.
The duplex mode 3 setting in an RTCM (menu 18) is complementary to app_rpt duplex mode 3. Rather than preventing a repeat audio path it provides one. In other words the RTCM performs in-cabinet repeat. This would be used to eliminate repeat audio delay. Duplex=3 must be set in app_rpt otherwise there would be two audio repeat paths and thus an echo.