Dampier should be able to bring some toughness, defense, and rebounding to the Heat. However, their big man rotation is a mess right now.
Basically, none of their centers can double as a power forward; you can't have Dampier, Big Z, or Anthony in at the same time as each other. That means you're stuck with Juwan Howard as your primary PF backup, which is far, far from ideal.
Now, when (or if) the Heat get fully healthy, Dampier will be a good addition, because they can run out a very good 5 man rotation of Dampier / Bosh / Haslem / Big Z / Anthony. Those pieces are largely complementary. However, by losing Haslem, the Heat are screwed until he comes back.