Yes you can sharpen the edge of a carbon blade, but it will never keep the edge for more than a few cuts, even i relatively soft material ...
... You will get the best results If you use only very fine weave low weight CF that is very densely woven (Like the EC Plain 130 gsm specialist) and A hard resin like EC IN2 .. You will need to use a mould that will stand up to compressing the edge area of the blade with high pressure. (And vacuum of course)
Also to make the blade keep its edge best, make the angle you sharpen it at , quite steep . do not try to make a very low angle like on a straight razor..
To make something really cool using CF, use a Titanium or stainless foil as the middle layer in the blade. Such a blade will actually be practically usable .. even if the foil itself can not be hardened.
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