If you have chlorobenzene, wont it undergo nucleophilic addition at the ortho and para positions?
Yes it will
Making it an activating group.
No.
These are two different effects,
directing effect and
ring activation. In most cases, they are related, because electron releasing groups will stabilize carbocations, making the benzene ring more active to substitution, and will stabilize the ortho and para positions preferentially due to their electron donating effect and resonance effects. However, for the specific case of halogens, the substituents are electron withdrawing groups and will destabilize carbocations, making the ring less active to substitution. But, due to the ability of halogens to contribute their lone pairs of electrons into resonance structures, the ortho and para positions are still more active than the meta position. Halogens are deactivating, because they make it harder to substitute into the benzene ring, but are still ortho/para directing, because of the resonance effects. For typical electron withdrawing groups, there are no available lone pairs to conjugate with the ring, and they are both deactivating and meta directors.
I would imagine that as the chlorines are added to the ortho para positions the rate of reaction would rapidly decrease.
Yes, which means the chlorine is deactivating. If it was an activating group, addition of more chlorines would
increase the rate of reaction. This is what makes addition of an activating group to a benzene ring somewhat difficult to control - addition of each activating group makes a product that is
more reactive than the starting material, and you tend to get multiple substitutions on the ring.