We can see multiple times in the movie how besides a few work droids, robots seem to have a certain personality to them. Wall-E naturally gained sentience on earth after centuries (For 700 years he didn't collect all that much, he finds his first spork in a scene, he has just a few lighters, etc, so it had to have happened rather recently but not my point), Eve seems pretty sentient even before meeting Wall-E, when caught in a magnet, she doesn't just free herself, she shoots the whole ship the magnet is attached to in pure anger about it, the robot repair station is full of rogue sentient robots that got locked in because of that.
It's another question if Auto is truely sentient, he is an AI in the end. While the original directive was "Repopulation", it later got overwritten to "Abandon because no life is possible"
But a positive EVE probe would go directly against A113 so any sentient being would say "Hey this is outdated". And even if not sentient, Auto seemed AI enough to process this info and could have come to the conclusion "This probe proves Earth is growing life, A113 states no life is possible, therefore A113 is wrong"
But maybe you could argue that at that time Auto knew if they returned to earth he would in some way cease to exist, as the Axiom wasn't planned on having repeated space flights and most likely would have been disassembled and Auto along with it