Physicist: Nope.
A blackhole is already the result of over filling. A blackhole is to mass as the rage virus is to people; throwing more at it just makes it more dangerous. However, unlike zombies, blackholes do eat each other.
The more matter that falls into a blackhole, the bigger the blackhole becomes. For example; the blackhole at the center of our galaxy (Sagittarius A*) has a mass of about 4 million suns, which is already the size of some small galaxies. Small globular clusters anyway.
If all the matter in the universe were chucked into the same giant blackhole you’d have: a really giant blackhole.
Is it known if Sagittarius A (or any other black hole) is already big enough to one day stop the expansion of the universe?
Or is the expansion fast enough to keep escaping the black holes?
The total gravitational attraction of a bunch of mass is a function only of the amount of mass. So whether the mass takes the form of a solar system, or a black hole, or a diffuse gas cloud makes no difference.
Black holes are only impressive if you’re fairy close to them. For example: if the sun were to suddenly collapse into a black hole, the Earth would continue to stay in exactly the same orbit.