Not necessarily, no...... I suppose it depends on your perception of active from behind......
I take the term 'on the bit' to basically mean on the aids and working from behind into a consistant contact of which the horse is totally accepting.
It's actually not acheived very often imho!!
No because being light in the hand could mean their head is in your face!!
Generally its is working actively from behind into a soft rresponsive contact with a softly swinging back over a rounded topline created from the horse beng correctly "engaged" from leg to hand....very generally!!!