If a prevailing wind traveled due east in the Northern Hemisphere, would the Coriolis Effect act on the water?

I am in a Marine Environmental Science II class, and we are discussing the Ekman Spiral. As I understand, the Coriolis Effect does not occur when whatever is observed does not change latitude. So, if a wind above the ocean in the Northern Hemisphere were to hypothetically blow due East, with no change in latitude, would the water under the wind still be deflected to the right in the form of the Ekman Spiral?

• The Coriolis effect acts even if you do not change latitudes. f=2*omega*sin(latitude), where omega is the rotation speed of the Earth (one rotation in about a day). Jan 31, 2018 at 15:50
• The only place that has zero Coriolis if you are going along a latitude line is exactly at the Equator Jan 31, 2018 at 16:17

As arkaia commented, the total deflection magnitude is $f=2{\omega}\cdot{\sin(latitude)}$, which is an orthogonal vector change (and as such shows up as terms in both the zonal and meridional velocity equations).