Not really. The tamper serves to keep the nuclear material together longer through inward inertia. Additionally tampers are usually neutron reflectors which als

Not really. The tamper serves to keep the nuclear material together longer through inward inertia. Additionally tampers are usually neutron reflectors which also reduce the time needed to burn all of the material into energy. An analogy I've heard is that without a tamper an implosion device would be analagous to resting a hammer on a nail and trying to push down on it. Including a tamper is analogous to raising the hammer and striking the nail. You accelerate the hammer head use the inertia of the hammer head to create a greater impulse to strike the nail. EDIT: More clearly answering your question yes the spherical implosion mechanism was absolutely critical for creating the needed material density for the bomb. I'm correcting the usage of calling it a tamper, as it is a separate piece of the nuclear bomb puzzle.