Records show that 99% of all species that ever lived on earth amounting to over five billion species are extinct. This is as a result of rapid environmental changes, changes that can only be blamed on man's reckless activities.
Earth's current estimated number of species are between 10 - 14 million with over 90% undocumented. Judging from this record, It is very clear that biological diversity will be greatly affected in an unfavored manner over the next 50 years. It's good to see that the world is beginning to come around the idea and taking steps to control it, or rather, slow it down.
Let's take a look at the point you made on a vast majority of species are yet to be discovered. I'll like to add that over 50% of those undiscovered species are believe to be aquaterrestrial with the remaining terrestrial in tropical regions which contains 90% of species known to us.
This goes to show that biodiversity is not evenly distributed on earth. For the success of any type of control measures, all hands have to be on deck, otherwise we'll face more mass extinctions than already recorded. But then, how can we begin to preserve biological life if we're unaware of it's existence? Even the ones we are aware of, we can't preserve them a 100% as our population is ever increasing with industrialized activities soaring to it's peak. Am afraid that no matter how hard we try, achieving complete preservation biological diversity is a lost battle.