Nope. We only see a vanishingly small number of species actually in the process of being collectively assimilated. In each case, those races put up a spirited but futile resistance (and with the exception of humanity and Species 8472, obviously).
Yes, kinda. In the novel Star Trek: Voyager - Unworthy we meet the Indign. These Borg worshippers have been attempting to contact the Borg (whom they worship as gods) in order to volunteer for assimilation.
Unfortunately for them, they were deemed "unworthy" of assimilation and bypassed. By the time we catch up with them, the Borg have been all but wiped out.
“Or we could remain in the system until the Indign are willing to
speak with us again, at which point we tell them the truth,” Willem
“That the Borg no longer exist. Their master race was conquered by an
even greater species and no longer occupies this area of space. Their
offerings are no longer necessary.”
“You and I both know that in a situation as delicate as this, sharing
that information could prove disastrous.”
“So we simply lie to them by omission? And allow them to go on
victimizing other sentient creatures in a cause that has gone from
irrationally motivated to absurd? That’s the Starfleet way?” he
“We have to respect their cultural norms, Admiral. They worship the
Borg, the same way humans worshipped gods in any number of forms for
thousands of years. It doesn’t matter that those gods are intemperate
and ultimately unknowable. That’s part of the allure for those who are
so inclined. It’s evidence only of their shortcomings, not those of
their gods. It’s the basis for faith.”