Yes, but the Wayne's were killed in a Romulan attack on Khitomer.
My idea for a 23rd century version of Batman is this;
Bruce Wayne is born to Thomas and Martha Wayne on a Earth colony world called New Gotham, in the Ophichus system. Once, New Gotham was a great colony, but it's become like Nimbus III, with the capitol city of New Gotham particularly affected and being somewhat rundown like Paradise City became.
Thomas is a businessman of great repute, and has built Wayne Enterprises into a great company that makes great technological devices, ably assisted by Lucius Fox, however, he prefers to work at the main hospital in New Gotham City. One night after attending an old movie (the Zorro movie starring Antonio Banderas) in the downtown district, he, Martha, and Bruce are walking back to their hover car, get in, and begin to drive back to their estate outside of town when all of a sudden, they are intercepted by space pirates attacking them in combat shuttles. They are forced off of the 'road' and made to get out of the car. The leader of said pirate band, Chesterfield Cobblepot, only wants to kidnap the Waynes, but underling Joe Chill panics when Thomas tries to protect his family and shoots him dead with his phaser, followed by Martha when she tries to back up her husband. Bruce could've ended up the same way, but the local law enforcement shows up, stuns Chill and the other pirates (Cobblepot was elsewhere directing the attempted kidnapping), and he's saved. His parents are still dead, and young Bruce is inconsolable.
After the funeral, Bruce maps a plan for his life: he studies a ton of science and technology subjects, becomes physically adept and proficient in all sorts of fighting skills, learns how to fly spacecraft and also starships, and studies how to be a detective. After many years away on Earth and elsewhere doing this, he returns to New Gotham determined to fight space piracy and whatever crime exists in New Gotham City. But how will he do it?
He remembers being scared by bats while visiting Earth, so he decides to use the iconology of a bat to frighten crinimals while fighting crime. He builds a Batmobile (think of the one from
Batman Beyond, but with 23rd century technology) that has cloaking technology which allows him to be invisible and to make getaways to Wayne Manor without being seen. He also builds a small starship called the Batwing, which has the same cloaking tech that allows him to 'attack' pirate ships without being seen initially (he only attacks a pirate ship to disable it, then he boards it stealthily to fight and disable the crew without killing them, much as Batman always does now.) His Batsuit is black and stealthy, allowing him to sneak up on anybody on planet and fight them in the manner of the original comic book hero, and it also produces a form of 'invisibility' to sensors so that local police, or anybody else, can't just detect him coming and going untill he wants them to.
As Bruce Wayne, he lives the life of a playboy enjoying all of the social things a millionaire playboy would do, but as Batman, he fights his never ending war against crime on the streets of New Gotham and in space.