The issue of vertical velocities under a ship is a very interesting question and not one that is easily answered. Several researchers have studied the problem in detail, both using current profilers and with ship modelling studies. From everything I have seen, it clear that this "apparent" vertical velocity is generated by the ship itself. In other words, the water dips down at the bow and comes back up at the stern. Pretty intuitive when you think about it. What is less intuitive is the depth to which the ship generated vertical velocity can reach. For large research ships I have seen traces of vertical velocity as far down as 50-m - but this obviously depends on the size of the ship (and to some degree also the speed).
One other thing to have in mind is the tilt; When collecting data, your vessel mounted system may be tilted and for this reason, a relatively large Vz component creeps into the data.
When we correct the data with the GPS/heading, we process the V_east and V_north components, but nothing is done wih the Vz term, which remains large.
The impact on the horizontal velocity is quite small and for the purpose of streamer handling (with low ship speed) it can be assume to be irrelevant. For scientific purposes, however, it can be of significance when looking at data very close to the ship. In other words, there is no need for concern unless you specifically want to use the vertical velocity data.