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You'll be able to predict this by taking appropriate measurements (will probably require a feeler gauge to check the clearance between the bearing and the flat face of the seat) and using trigonometry.
Or you could just hold the bearing on the crown 'race' and hold it up to the light to see if you have any gap to play with.
If cutting a slot in the 'race' won't work due to no or insufficient gap to make it work as a collet, maybe try this before you take the scissors to the beer can:
BITD when I used to volunteer at a community bike workshop, we'd get this all the time. I developed what seems like a terrible kludge which actually turned out to be quite robust - just use sellotape. Take note of where you start so you can stop just short of the spot to keep it round, and pull it tight to reduce its compressibility. Apply more than you'll need and remove layers as necessary until you can just squeeze it on without tearing up the tape. It'll be pretty solid when it goes on, and should actually last pretty well, surprisingly enough. I think maybe the combination of pressure and time makes it go a bit hard?
Obviously, if you need to build up more than half a mm or so, the tape will want to start creeping around... You could try other tapes, but you've gotta find one with a good trade-off of resistance to compression against resistance to tearing as you fit the crown race. Aluminium tape is the only other tape I've tried which can work, but the ones I've come across are tediously thin.
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Kimmo
snottyotter
Google "split crown race". Loads of cartridge bearing headsets come with split crown races, the chamfer transfers axial load into radial compression of the "race" (collet) so the higher the axial load, the tighter the collet grips the steerer. This is also how the preload adjuster at the top solves the issue of the upper bearing collet not being a press fit on the steerer.
The simple machine which does this is called a wedge (in this case wrapped into a cone)
Of course, you could be right, if the difference between the diameters is so great that the bearing bottoms out on the flat face of the seat before the collet has shrunk enough to grip the steerer. You'll be able to predict this by taking appropriate measurements (will probably require a feeler gauge to check the clearance between the bearing and the flat face of the seat) and using trigonometry.