If so, does this imply that there is a change in the max and min tide heights in the estuary or is the tidal height unaffected?

Answer: this depends... If conditions in the inflow channel offer relatively high resistance to tidal inflow, the upper portion of the estuary may not have come to equilibrium with the elevation of the high tide before the tide begins to recede. Consequently, the upper area does not reach the full height of the tidal staging. Neither does the upper area fully drain to the stage of the low tide before high tide begins. Under these natural conditions, specific environments develop within the upper area of the estuary, and in the fore-beach oceanward section of the estuary outfall where the outflow reaches and mixes with the sea. But if the channel is deepened, less hydraulic resistance to this inflow and outflow is present and the interchange of this water becomes more efficient. The range across the max and min tide heights may be affected. This can have adverse consequences to the estuarine environment.

How does this effect the rate of water flow?

Answer: Dredging will improve the water inflow and thereby increase the rate of inflow and outflow in response to tide. This is because deepening of the channel reduces the channel's hydraulic resistance and thereby improves (increases) the rate of inflow, and outflow. Depending on the size of the estuary, and the response to tidal inflow and outflow, the expected consequence would be that somewhat more volume would accrue on the inflow in response to high tide.

What other hydrographic effect might occur?

Answer: This is unknown. In some instances the consequences can be dramatic. For example, estuarine marshland can be adversely affected by the post-dredging influx of more saline water.

Disclaimer: This answer is in regard to general observations, only. No consultation or practice liability is assumed.