It depends on what you mean by "dominate".
Fans in series add their static pressure curves together.
As Chris correctly points out, conservation of mass applies, since neither fan has the mystical ability to either create or destroy mass.
So, from the supply fan's perspective, it doesn't know that there is or isn't an exhaust fan. It simply knows it's inlet and discharge pressure, and operates at the corresponding point on it's fan curve.
If there is an exhaust fan, the supply fan's discharge pressure is lower than it would be if there is not an exhaust fan, so the supply moves more air.
Same, but opposite, for the exhaust fan.
If the fans are seriously mismatched, say for example the intake fan >>> exhaust fan, then the intake fan will simply blow through the exhaust fan. It may even turn the exhaust fan's motor into a generator, but both fans will still be operating on their system curves (although generator portion of a fan's operating envelope is generally not published).