Not always and not everywhere.
(But the risk was there in Scorpion, so blocking the nanoprobes was definitely going to be a top priority. They just couldn't be absolutely certain (Warning: TVTropes) of the actions the Borg would take.)
During Voyager, when their motivations are looked at more closely, it's established that the Borg are chasing some sort of ideal of theirs, that they call "perfection". Assimilation is meant to add to their perfection by incorporating unique elements from various species' biology and technology. But first, they have to identify such uniqueness.
First, a couple quick quotes about perfection as it pertains to the Borg:
VOY 4x01, Scorpion, Part II:
Seven: They [Species 8472] are the apex of biological evolution. Their assimilation would have greatly added to our own perfection.
Movie, First Contact:
Borg Queen: We too are on a quest to better ourselves. Evolving toward a state of perfection.
Data: Forgive me. The Borg do not evolve. They conquer.
Borg Queen: By assimilating.. other beings into our collective, we are bringing them closer to perfection.
Initially, that would make it sound like they would assimilate everyone, in order to bring those individuals closer to the Borg's perfection (as described by the Borg Queen), but that is not necessarily the case. There is another exchange in Scorpion, Part II that indicates the Collective as a whole doesn't usually bother with what they consider insignificant:
Janeway: If we create smaller weapons using our torpedoes, and destroy a few of their bioships, it may deter them, convince them to give up this war.
Seven: You are individuals. You are small, and you think in small terms. [very long pause] But the present situation requires that we consider your plan.
The Borg think on a large scale. Entire species and civilizations, in order to make leaps and bounds in attaining their perfection, rather than making effort for very small gains that may or may not be worth it.
Even then, entire species can be deemed unworthy or unremarkable. For example, the Kazon (as described in VOY 4x12, Mortal Coil):
Seven: The Borg encountered a Kazon colony in the Gand Sector, grid six nine two zero.
Neelix: Were they assimilated?
Seven: Their biological and technological distinctiveness was unremarkable. They were unworthy of assimilation.
Neelix: I didn't realise the Borg were so discriminating.
Seven: Why assimilate a species that would detract from perfection?
The general point I'm trying to get at is that before the Borg assimilate anyone, they first find out if it's worthwhile.
- Single individuals are rarely going to be worthwhile, because usually very little can be gained from getting a few new drones. They're all connected to the same Collective.
- If those individuals are deemed a threat, there is now reason to destroy or assimilate them to protect the Collective (such as what happened to Seven's parents).
- If those individuals indicate their species would be beneficial to the collective, there is now a reason to chase down their entire civilization (what appears to have happened with Species 8472).