It will take a while till the animal restores the blood levels of the protein and during that time amount of neurogenesis is going to be lower.
But maybe when you're young, having it occasionally filtered would induce a higher set point for production.
Might be true when you're old too.
In experiments performed on mice, blood transfusions from young mice reversed age-related markers in older mice. The protein involved is identical in humans.
http://mic.com/articles/88851/harvard-scientists-may-have-just-unlocked-the-secret-to-staying-young-forever