Even if I bought that such a projected population drop were going to occur (I can see how something like that could happen, but I doubt anyone's forecasting and modeling is solid enough to state such a prediction as if it were inarguable objective fact), humans are likely to prove to be very robust as a species, even if many individuals die off by the billions.
Suppose humanity has to contend with Malthusian crashes and booms. We'd still be likely to rebuild technology during every boom, probably faster and further than the previous cycle since plenty of information would carry over from one cycle to the next. Further, even right now, not having to consider that kind of distant future, it's much more a matter of willingness to commit the necessary resources than our current level of technology that holds us back from having colonies on the Moon and on Mars.
A discovery that could lead to massive quantities of cheap, clean energy might just be around the corner even now. And if not so soon, it's certainly absurd to insist that in a hundred or a thousand or ten thousand years such a discovery simply can't and won't be made. Cheap, plentiful energy would solve practically all of the current problems of spaceflight, most of which are based on trying to travel through space on the slimmest energy budgets possible. If you've got lots of energy, you can fly fast, direct paths, you can carry plenty of supplies, you can lift and propel heavy spacecraft with plenty of shielding against radiation, etc.
The only significant doubts I have about humans spreading throughout space is that we may reach some sort of scientific/technological/biological "singularity" before we manage to spread very far. What would become of humanity after such a point (if anything which can still be called humanity were to exist at all) is impossible to predict.
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