Areas where topography prevents the outﬂow of water are called closed basins. Is the GAB a closed basin? What if external bodies of water flowed in? Is that still "closed"?
In the far north of the Great Artesian Basin, there is groundwater outflow to the Gulf of Carpentaria. Everywhere else the aquifer behaves as a closed basin with outflow in the form of vertical seepage (e.g. to the Mound Springs of South Australia), artesian overflowing boreholes, and pumped boreholes. There may once have been hydraulic connection to the Southern Ocean, but that ceased several millions of years ago - not such a long time when one considers that the longest through-flow time of groundwater, from east to west, is about two million years.
One cannot discount the fact that the northern islands of Indonesia Timor island and Papua New Guinea are very high precipitation areas. It has been documented that there is high groundwater movement under Sahul shelf off Timor Island. The same Sahul shelf is also between Papua New Guinea and Australia. Since there is high groundwater movement off of Timor Island there is a high probability there is between Cape York and Papua New Guinea shore line. So GAB could be replenished by the Northern Islands of Timor and Papua New Guinea.
Most of the underlying strata beneath the Gulf of Carpentaria seabed is part of the Great Artesian Basin (GAB). It extends out to the Arafura Seabed and west of the Torres Strait islands. It may even extend or connect with paleochannels of Papua New Guinea's (PNG's) coastal areas. Geoscience Australia has maps showing the northern borderline or "country" maritime border areas of GAB. One could assume that GAB probably goes all the way to the PNG coastline. CSIRO and Geoscience do not provide maps detailing the geology under the Arafura Seabed or Torres Strait seabed close to the PNG coastline.