Is Borg intelligence based on the sum of all the parts (people) in the collective, or is there a base personality that is imprinted on newly assimilated persons?
The Borg only assimilate species that will improve the collective. For example, the Borg do not assimilate Kazon (from Voyager). Likely the Borg would ignore a planet of idiots, or, if they were in some way a potential threat then the Borg would probably destroy them.
As Seven states in 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?
NEELIX: Good point. Well, if you'll excuse me, I'm needed in the shuttlebay. Pleasant regenerating.
I would say: no.
Even if they did assimilate a race of idiots (Xantec suggests they wouldn't, and with good cause), Borg intelligence is actually based on the sum of acquired knowledge and its logical application, not the people that make up the race assimilated.
As knowledge is abstracted from the host race, there may be a collective dip in accuracy while the new 'knowledge' is analyzed and integrated with existing, however I believe (and I can't think of any canon that supports or contradicts it), that the Borg would throw out (or re-categorize) any misinformation that counters valid knowledge.
The answer must be No. The Borg take the best of both worlds, not an average.
The collective has the sum of the species, not the mean. So even a planet of idiots would have something to add to the collective. Even if it may be a small amount.
They tend not to assimilate people who cannot add anything to their knowledge, whether they are stupid or clever. It is not the absolute level of intelligence of the assimilated, it is whether they can improve the race in some way.
The Borg Collective is essentially a huge Beowulf Cluster - a massively parallel array of low power computers to build a highly capable mainframe class computer system.
At present, the best supercomputers in place are outclassed by a cluster of videogame consoles... for a tiny fraction of the cost.
The Borg makes use of their synaptic processing - in other words, their brains - as a tool for massive computing. Plus, it augments their brains with linear computing via cybernetic interfaces. Plus, it dominates their behavior by implants being able to override the motor system of the brain. We know from Voyager that the mind is still present, and somewhat active, but subjugated during the drone's activity cycles, especially if resisting the collective in any way.
The individual idiotic individuals have to have some survival traits - even if it's only being able to breed quickly - and if dumb enough to be individually a liability, will be used as controlled drones for high risk tasks, completely bypassing their higher brain non-motor functions. Even so, bodies provide a resource. So think of them as people using old off-brand 80286 based computers running a lame version of linux... and being happy... then the big bad borg botnets them and viruses them so that the keyboard isn't used, just the video cards and printers, and the off-switch doesn't work.
Also - keep in mind - YOU have been personally botnetted any time you use a recaptcha authentication... one of the two is a known word; the other is one that recaptcha's OCR didn't recognize. You don't have to be bright to do that task, you just have to have synaptic symbol recognition, which is really hard to implement on computers, but is inherent in humans, and quite probably, also in any other social tool-using language-using species.
Even the Pakled.
And I think I saw a Borgified Pakled in the background on an ep of Voyager...