Dark matter is generally believed to be dark because it only interacts with "normal" matter through the weak (and gravity) force. It is interacting, but only weakly so.
BECs interact strongly with normal matter. Indeed one of the problems with making BECs is stopping their interactions with the experimental apparatus from destroying them.
As Ron says, dark matter could form a BEC, at least in patches, but it wouldn't make any significant difference to it's effects on the rest of the universe.
Response to Clive's comment:
As anyone who has watched the Discovery channel will know, there are four forces: electromagnetic, strong, weak and gravity. Normal matter (by normal I mean the stuff around us) interacts using all four forces, but it's conjectured that dark matter does not interact with the electromagnetic and strong forces i.e. it only feels the weak force and gravity. Dark matter was first suggested precisely because in galaxies and globular clusters the gravity seemed to be higher than it should be, so the gravitational interactions of dark matter are extremely important on the large scale. However when you're looking at individual particles the masses are so low that gravity can be ignored, and you're left with just the weak force.
Actually the weak force isn't that weak, but it's extremely short range so two particles interacting by only the weak force would have to get extremely close to interact. The best known of the "weak force only" particles are neutrinos, and they can pass through the entire Earth and hardly notice. Detecting them at all requires enormous detectors like Super Kamiokande. Dark matter particles are expected to interact as weakly as neutrinos, hence the great difficulty in detecting them.
Re the Bose Einstein condensate: a BEC is made from normal matter, but the atoms in it need to be cooled to extremely low temperature so they all fall into the lowest quantum energy state. The spacing between energy levels in a typical BEC is small, so even a small amount of energy will raise atoms above the ground state and destroy the BEC. That's why they are so hard to make. The first BEC had to be cooled to 170 nanokelvin. That's 0.00000017 degress above absolute zero!
A BEC made from dark matter should be easier to make, because it wouldn't be excited and destroyed by passing photons (because photons don't interact with dark matter). With normal matter you need to take extreme care of your BEC.