Yes and No.
You do go to the level specified in the Next Level Setting, but it counts up gems and stuff first, and before that there's a bit of a wait as well (in case there's Endtext, I guess). Also, defeating the Queen will not send you the next level UNLESS SHE FALLS ON SPRINGS (maybe just red springs.. I'm not sure I've ever tried). Also, as a general rule, the boss must be activated first.