A good summary of the Zerg race is given on wikipedia as follows:
The Zerg are a collective consciousness of a variety of different races assimilated into the Zerg genome. The Zerg were originally commanded by the Zerg Overmind, a manifestation of this hive mind, and under the Overmind's control the Zerg strove for genetic perfection by assimilating the favorable traits of other species.After a species has been assimilated into the Swarm, it is mutated towards a different function within its hierarchy, from being a hive worker to a warrior strain
In other words, if the zerg see some biological feature they like, they assimilate the creatures that possess that feature to evolve into more adaptable creatures.
Furthermore, the starcraft wiki goes into some details about the Zerg's genetic structure:
zerg genetic material consists of DNA, seemingly in the shape of a double helix. However, when a zerg strain's DNA evolves, it becomes less flexible. -http://starcraft.wikia.com/wiki/Zerg
The question is, given what we know about biology and evolution thus far, would it be possible for such a race of aliens to exist in the real universe?