If the Oort Cloud had been teeming with VN probes for (presumably) a couple million years, we would know because they would long ago have expanded into the inner Solar System. We would see them swarming in the asteroid belt, the rings of Saturn, in orbit around Earth itself.
The whole point of the Fermi Paradox is that if spacefaring alien life behaves as life does on Earth -- expanding into every habitat it can, transforming those habitats in the process -- then we should not have to go looking for it. It should have colonized us already. There are three solutions:
1) Spacefaring alien life does not behave like life on Earth.
2) Spacefaring alien life doesn't exist.
3) It has colonized us already, and we just can't comprehend what's right in front of us.