As detailed by “Sorry!” Interbreeding of closely related species is all but impossible ... there are many examples of hybrids in all "higher" taxa even in the well known mammals. E.g. within the same genus (Tigon / Liger) and in different genera (Rhinos black x white), false killer whale x dolphin (http://en.wikipedia.org/wiki/Wholphin" )… . Some older Zoologists continue to ignore this, while most Botanists never adopted the “biological species” concept of Ernst Mayr. Strict hybridization barriers between closely related and therefore to some extend genetic similar, but in a morphological sense clearly different species, might - or might not be present.
Even very unrelated species can exchange DNA (This isn't "interbreeding" in a common sense) see this http://www.wired.com/wiredscience/2010/01/bornavirus-in-human-dna/"
But to come back to your question: Convergent evolution is the result of similar selection on phenotypes due to shared environments or lifestyle ... so certain parts of the bodies in unrelated taxa get similar during convergent evolution, as certain forms are advantageous in a certain environment. Convergent evolution will not result in two unrelated species being the "same" in every aspect, as other parts of their bodies will not undergo convergent evolution and stay different. E.g. despite being adapted to flying, bats never evolved the beaks of birds, or their elaborated breathing system. Two species being too similar to each other in morphology and lifestyle will result in large ecological similarities, which will cause heavy interspecific competition and result in extinction or geographic exclusion. So there is even a mechanism that hinders unrelated species in being too similar. E.g. it’s highly questionable whether dolphins could have evolved in the presence of ichtyosaurs as the dolphin niche was already occupied by the very similar ichtyosaurs.
While phenotypes will get similar during convergent evolution, there is no reason to think that genotypes will evolve more than random similarities. Therefore interbreeding of birds and bats, whales and fish, or ichtyosaurs and dolphins is highly unlikely and as said by Borek:
Borek said:
For all practical purposes impossible.