No. The Queen should be seen as the manifestation or personification of the Borg collective mind, not the "brain" which normally houses the entire collective and commands all drones. The Queen is a female drone that can be used when the Borg feel interaction with other species needs to be through a more personal approach, such as the temptation of Data and Picard. The writers have admitted that the Queen was a plot device for this purpose, as a disembodied voice alone would not have been very persuasive. If the Queen in First Contact was indeed the controller of all Borg, that would mean that the Borg in the 24th century would immediately be without a consciousness as soon as the Queen travels back in time and doesn't return. However, this doesn't happen, as the crew of the Voyager also has several run-ins with the Borg and the Queen, and the Queen can be resurrected each time. It is interesting to note that when the Queen is destroyed in the plasma, the other Borg drones immediately malfunction and power down, suggesting she had taken total control over those drones when they were separated from the rest of the Collective. However, in the Enterprise episode Enterprise: Regeneration (#2.23), which takes place a century after First Contact with the Vulcans, a few Borg drones are recovered from wreckage of the Borg Sphere that ended up on the North Pole. After thawing out, they quickly regenerate and form their own mini-Collective, seemingly without ill effects from the Queen's destruction 100 year earlier. In the episode Star Trek: Voyager: Dark Frontier: Part 2 (#5.16), in order to escape, Captain Janeway destroys a Borg power node, which (temporarily) disables the Queen's command interface and thereby her control over the Collective; however, this does not stop the Borg from laying in a pursuit moments later. These examples all illustrate that the Queen is an important, but by no means essential part of the Borg Collective. Some writers of non-canon Star Trek novels have even suggested the Queen is a separate program within the hive mind and can be implemented as the need for a single-acting drone arises or even as a signal booster to connect Borg that are spread out over many light years.