^Did the Borg know that? They clearly wanted something from the Federation, or they wouldn't have bothered with them in the first place. They took Picard because they wanted a spokesperson who could relate to humans, but that had nothing to do with Starfleet's technology or equipment.
The way I see it, the Borg went back in time in FC so they could send information about the future to the Borg of the past. I base this on the following points:
- Apart from a few shots fired towards the surface when they first arrived, the Borg did nothing at all to stop Z's flight until AFTER the deflector dish was destroyed. Once the dish is destroyed, the Queen tells Data, "There's been a change of plan," and the Borg start trying to stop Z again.
- And what were they doing with the dish anyway? Calling for reinforcements? The Borg didn't need reinforcements, Humanity was in terrible shape. And anyway, they could easily assimilate people to increase their numbers. it's far more logical to me that the deflector dish was an attempt to send the 21st century Borg information about the 24th century Federation and/or 24th century Borg.
So, the message that the Borg send tell the Collective about the Federation gets the Queen in the 24th century curious, and she sends two ships. The first is the one that the Hansens found and followed back to the DQ. The second is the one we saw in Q Who. It comes along, assimilates a Federation outpost and some Romulan outposts (The Neutral Zone), then figures that Humans and Romulans aren't very different to what the Borg can find back in the DQ. And it's a waste of resources to go halfway across the galaxy to get something you can get in your own backyard. So the ship starts back home.
But then Q flings the Enterprise into the Cube's path, and the Borg are all of a sudden, "How did this ship get out here?" They try to assimialte it to find out, but then Picard says he needs Q, and Q sends the Enterprise back to the Federation.
The Borg figure that the Feds have some cool engine technology that they must have missed, and the Cube turns around and heads back towards Earth, and we see it again in BoBW.
Also, I never bought the idea that the Borg wanted Picard as a spokesman. What, only a Human Borg could say, "We will assimilate you, resistance is futile?" I think it's more likely that the Queen wanted to use Picard as an example, as a way of showing how much power she had over the Federation.