From my experience (having been both on the manager's and the associate side) I know that most managers do not report the estimate given by their employees up to the next level. Instead they go by their own gut feeling + knowledge of the external constraints.
When manager asks for an estimate, he/she often cares less about the estimate value itself as much as about associate going through the analysis and figuring out subtasks, major gaps, dependencies, etc. In other words, asking for the estimate is often a trick the management employs to get the employee going. In this case the estimate value is just a dependency injection mechanism to force the employee to do the analysis.
Of course tricky managers also tend to remember the estimate value, especially if it was an underestimate and use it to control the urgency level on the project.
