Yes, you are right.

The velocity will be the sum of the electroosmotic and electrokinetic velocities, but the walls and particles will probably not have the same zeta potential.  If the channel is open at both ends, electroosmotic flow is unidirectional; if closed, central velocity will be in the opposite direction of wall velocity.  Either way, electroosmotic velocity will follow a parabolic pattern across the channel and therefore so will the particle velocity. 

@Paul Wilson Todd

Thank you for the insightful answer, Paul. One thing I don't understand is that how can a osmotic flow profile form a parabolic pattern in an open channel? (instead of a plug flow). When closed, I understand it should be parabolic because a pressure driven flow should balance the osmotic flow, hence parabolic. But when the channel is open, I believe the osmotic flow should be the only driving mechanism for the flow, which should be plug-like flow (as long as the channel width is greater than electric double layer). I'm a bit confused to your point.

Sangwoo, you are, in general correct.  Plug flow of an aqueous solution would be expected in an open channel of appropriate dimensions and at appropriate ionic composition and viscosity -- very likely the case in a typical microfluid situation, in a several-micron channel with a few nanometer double layer. 

Thanks a lot, Paul!