Not exactly, but it may depend on which "interpretation" of bel canto that you are referring to. The cornerstones to the Bel Canto technique are the "inhalation of the voice," the "hold of the breath," and the mask of the face.
Inhalation: The sound is actually drawn in from outside the body, with a stream of air hitting the hard palate, and passing over (not through) the vocal cords, and into the sinus cavities. As the air passes over the vocal cords, it creates a difference in air pressure, much like when a truck passes by and pulls everything along with it, and draws air up from the lungs as it passes over. The air that is drawn up from the lungs passes through the vocal cords, creating the sound. The inhaled breath bouncing off of the hard palate creates projection, and the air going into the sinus cavities provides resonance. Caruso wrote (quoting roughly), "sing as if continuing to take in breath."
Hold of the breath: The diaphragm is pulled down in order to take in breath, so that there is adequate air to be drawn up from the lungs. With as much air in the lungs as possible, there is a strong "foundation" on which to support the breath. As a result, the goal is to (roughly quoting again) "maintain the diaphragm as if holding one's breath." Air WILL escape from the lungs, as if it doesn't, no sound is produced. A more controlled amount from the lungs (minimal) will allow for more contol overall, and a stronger foundation will result in a more "supported" sound.
Mask of the face: This is pretty widely used in many techniques. Essentially, the higher notes are wide across the cheekbones, and the lower notes are in the bottom point of the inverted triangle, which puts them just in front of the lips and very narrow.
Chris