Firstly, it wouldn't have worked.
The Borg would have just thought, "We'll, I've been looking at it for three years now, and it's obviously a paradox. I'm gonna stop now."
Besides, if a paradox could destroy the Borg, they would have encountered one long before Picard came along.
And if it really would work, why not just send a different ship out with a captain who wouldn't balk at it?
And for the record, here's my interpretation of the Borg timeline with the Feds.
- Sphere is destroyed in Earth orbit just before Zef's warp flight.
- A century later, the research team comes across the wreckage of the sphere and defrosts some drones. They end up transmitting a message, and it will take the Borg 200 years or so to receive it and then come and have a look at this Federation thing.
- A long time later, the Hansens go to investigate the Borg after hearing rumours etc. They end up being zipped to the other side of the galaxy and being assimilated. No one in the Federation knows about that for a long time though. As far as they are concerned, the Hansens just vanished.
- Tombaugh is assimilated. Again, its disappreance is a mystery.
- Q Who. And we know the rest from there.
I think that works pretty well.