For the new guys, this is old hat for the "old timers". In my experience, using one of my lowers, a missing or collapsed disconnector spring will cause full auto fire. If you keep the trigger pulled with a connector missing or a connector spring missing, the BCG will continue to cycle. An upside down spring stuck down will do the same. As long as the trigger is pulled, just like a M-16, the rifle will continue to cycle. Once the the trigger is released the trigger catches the hammer and the rifle stops cycling. With the spring missing or sticking, bursts may be intermitten if the disconnector happens to flop forward during the process and catch the hammer.
I did not try this with live fire, merely testing the mechanics of the FCG. It consituted a function test with the disconnector missing and then with the disconnector spring missing. The function test failed in both conditions.