
If you pose this question through Google the answer is pretty quickly returned as “no they do not”.
Now why might that be?
To understand why we need to consider the environment they had before humans came ripping through their homeland and changing everything.
Koalas are arboreal marsupials which means they live in trees, and are mammals that give birth to tiny under-developed young that crawl into a pouch to complete development for around 6 months.

However, we need to think of incredible old growth forests thick with tall trees when we think of the arboreal koala. When you live high in the canopy of a forest, there is not a lot you can see long range. The ground is distant and hidden by the lower branches and smaller young trees. Anything beyond the tree you are in, is likely obscured by branches and leaves from your tree or the next.

Koalas are far from blind, but their long range sight is pretty poor because it was not needed. Koalas are skilled at jumping from trunks and branches to move about, and they look carefully to judge the distance before taking a leap.
Koalas have an acute sense of smell, and they do have keen hearing. Sometimes it seems their hearing is not so keen because they sleep so deeply.
If you can imagine huge forests with hundreds of koalas moving through the treetops, you can maybe imagine that they didn’t bother looking to the ground or out into the sky too often. Their focus was within the short range area of the tree they were currently occupying.
Koalas are said to have no natural predators, but this isn’t completely true. However the only predators that were of any real concern to koalas in the past were usually only a concern for joey’s and small juveniles, and only if they were not in the treetops. The main predators that may take a small number of young koalas are goannas, dingoes, pythons and some powerful owls and eagles. The incidence of these predators seems to have always been fairly low. Coastal pythons are the only one of these predators that may attempt to take a lone young koala in the canopy.

This all means that koalas do not have a historical need to be on a constant lookout for predator threats, and they do not hunt as predators themselves, and so their eyesight, for long distances is somewhat poor.
Another important feature of koala sight is that their eyes are ‘forward facing’ like our eyes. This puts the koala outside the general rule which says – ‘eyes to the side, run and hide; eyes to the front, love to hunt’. Koalas don’t hunt, and yet they did not have any real need to run and hide either, and so they have eyes that face the front which give better depth perception. It’s also one of the features that makes them look so endearing to humans.

The impact for koalas in adapting to the environment we have created by invading their home is huge when you understand their eyesight limitations.