I don't see why not, but Batman has encountered telepaths before, and has shown to have enough mental stregth and discipline to throw them off, at least temporarily.
The only story I can think of that addresses this question directly is "Identity Crisis" by Peter Milligan, a Detective Comics issue from the early 90s. It begins when Bruce Wayne wakes up to find himself by the river, almost having drowned. He can't remember what had happened the previous night, and returns to Wayne Manor wondering if someone had sussed his identity and tried to kill him. When he returns, he's shocked to find that Alfred has no idea who "Batman" is, and neither does Tim. There is no Batcave, just an empty cellar. He discovers while watching the news that someone else is Batman, and buys some mountain gear and tries to track him down. He fights whoever the imposter is, but is equally matched. He returns to Wayne Manor, where reality is beginning to waver. Batman follows him, and takes his mask off, to reveal.... Bruce Wayne. The "Bruce Wayne" from the beginning of the story is actually The Synaptic Kid, a psychic who tried to read Batman's mind and suss his identity, only to find Batman's mind was too strong. He got confused, and awoke in a split reality where Bruce and Batman are seperate people. So Batman had defeated him by splitting himself into his two seperate, distinct idenitities. At the end we learn that the Synaptic Kid is in a coma, under observation by doctors.
Any fan of the Animated Series willl find the description of this story familiar, and despite a very different outcome, it definitely inspired "Perchance to Dream".
