The Athabasca Valles outflow channel system is among the youngest such channels on Mars, with the Athabasca Valles flood lava (AVFL) covering the channel floor and reaching far beyond. Volcanic rootless cones on the AVFL indicate the presence of H₂O in the shallow subsurface at the time of lava emplacement. However, Athabasca Valles are near the equator, where ice would rapidly sublime in the current climate. Therefore, the source of water for the rootless cones is uncertain: the leading hypotheses are that it was deposited (i) from the atmosphere in a different climate, or (ii) by a large aqueous flood shortly before the lava was erupted. Here we test the aqueous flood hypothesis, using numerical models of floods traversing Athabasca Valles to determine whether they can provide water to the locations of observed rootless cones. A secondary test is to determine whether flood waters are available to carve Lethe Vallis, a distal channel likely carved by the same event that formed Athabasca Valles. We find that floods with volumes and fluxes based on previously published estimates are unable to reach the distal rootless cones or Lethe Vallis. This suggests either that the climate allowed equatorial ice to be present in the subsurface at the time of the AVFL, or that geologically recent aqueous floods in Athabasca Valles were much larger than indicated by published models.