The speed of sound is the velocity a force can propagate in a medium, so yes even assuming such a mega structure is theoretically possible (it’s not) it would close its mouth at the speed of sound.
If you want a galaxy-doom monster, either pick a super massive black hole, a super massime white hole, a super massive black hole coming out of a bigger white hole, or a super massive quasar pulsating high energy X-ray bursts with enough power to kill all life of an entire galaxy