Yes, but the Coriolis effect is important during the birth of the storm. Beyond that, the implication of your statement is that cyclones and hurricanes reverse direction as they cross the equator. I don't believe that is the case.
Hey NoNukes, This is correct but also incomplete. Coriolis is important during the formation of any any pressure system, High or Low, but together with other factors (Pressure Gradient Force, speed of rotation of the planet, rate of movement of the air mass, etc. remains a dominant effective force throughout the entirety of the system's life cycle.
The strength of Coriolis varies with the Sine of the latitude and is effectively zero at the Equator. Straightline winds can and certainly do change direction as they cross the equator. For example, the SouthEAST Trade winds in the Southern Hemisphere become the SouthWEST Monsoon winds that blow over much of western Africa in the Northern Hemisphere. They annoyingly help generate massive clusters of thunderstorms that drift west off the African coast as Easterly Waves that often become these tropical revolving storms.
But during their passage across the Atlantic, Coriolis deflects the entire system to the right (in the Northern Hemisphere), usually in conjunction with the Bermuda High (Clockwise rotation). So because of Coriolis you will almost inevitably see Tropical revolving systems move AWAY from the equator, not towards it. In the very rare event that a tropical revolving system is forced across the Equator, it would be more likely that the revolving motion would be entirely dampened.
Again, I'm not a real Meteorologist, and could be wrong, but I don't think I am in this case.
"...heck is a small price to pay for the truth"