Yes it's possible. The question is - should you?
From Wikitravel:
To climb or not to climb
Uluru is sacred to the Anangu people of the area. They say that the
climb follows the track that the ancestoral Mala men took to get to
the top for ceremony. They say that when you climb, you are on their
tracks.
In addition, there are some safety and environmental concerns - at
least 35 people have died whilst climbing Uluru - albeit most
accidents occur when leaving the marked trail. There are no toilet
facilities on the track or on top of Uluru. As a result, bacterial
levels in the waterholes at the base of the rock are significantly
higher then those further away from the rock.
The climb is also closed for various reasons; From 8am in Summer
months (December, January and February), Heat (if temperature reaches
36 degrees), Rain (greater then 20% chance of rain/5% chance of
thunderstorms in 3 hours), Wind (Speed at summit reaches 25 knots),
Wet (if 20% of surface is wet after rain), Cloud (if there is cloud
below the summit), Rescue (if there is a rescue from the rock), or
Culture (if the traditional owners request closure, for example during
mourning periods).
The decision to climb when it is open is yours - but make sure you are
properly informed before you decide. Visit the Cultural Centre first
to learn more about the park and what makes Uluru so significant.
Around the mountain you have a few options:
- The climb. If you have decided to climb, the best bet is to start early - the climb will be closed if the temperature is forecast to be hot. It is about a 1km walk to the top following a worn path with a chain. Remember there are no toilet facilities on the walk. If you aren't persuaded by the cultural arguments, then the view from the top of the rock is nice, and worth the climb. The walk is steep, but if you are fit, stay to the track, carry water, and avoid the heat of the day, it should present no extraordinary hazards.
- The Uluru base walk (9.8km) and will take 3-4 hours. Most people walk clockwise on the track but a few kilometres along this track the crowds thin out to just an occasional walker.
- The Mala Walk (2 km) This track begins at the Mala Walk car-park and ends at the inspiring Kantju Gorge.
- The Liru Walk is a walk between the cultural centre and the base of Uluru. It's 4km and takes about 1 and a half hours.
- The Kuniya Walk is an easy 1km walk to the Mutitjulu Waterhole on the Southern side of Uluru. There is some rock art here also in the rock shelter, and a good place to learn about the Tjukurpa (pronounced Chook-a-pa) of the area.