No, you don't always need an even number of centrifuge tubes when loading a centrifuge. The number of centrifuge tubes required depends on the specific design of the rotor. As long as the weight is symmetrically balanced across a centrifuge rotor it is OK to use any number of tubes.
More important than symmetrical loading is mass loading however. The centrifuge tubes should always have an equal amount of mass directly across from them in a rotor. In practice the easiest way to achieve this is to use an even number of centrifuge tubes, which is why for practical reasons most people use an even number of centrifuge vessels. Don't have an even number? No problem, simply fill an empty centrifuge tube with water to match the weight of the centrifuge tube directly across from it on the rotor. No need for expensive counterbalances, an empty tube and tap water will do.
