Pretty certain that's impossible.
I'm no expert on the i3's, but they are straight up dual cores, there's nothing extra in there to unlock.
I do seem to recall once hearing that some i3's (More than likely the higher tier end) feature lesser binned i5's with two cores disabled or otherwise unusable, but I doubt very much that would become a reality in your case.
As for overclocking. No, you can't do that either. Every i3 is locked at the point of sale. Such a lock is very difficult and in most cases impossible to get around.
Besides, even if you could overclock, you'd need to buy a beefier cooler, which would negate the money saved on buying an i3 in the first place.
If you plan on gaming with this setup, watch out for games...