This Houdini is the Houdini: the first escape artist, the guy who could wriggle out of chains and submerged coffins without breaking a sweat. He's brilliant, insane, talented and (at least in Doctorow's hands) has some very weird mama issues.
Houdini is portrayed as a typically head-in-the-clouds artist. He is affected by the changes happening in society, but not as much as those around him. His real interest is in pushing his escape feats further. He likes progress, but only because it means that he can experience the world through those amazing newfangled aeroplanes.
One of the interesting things about Houdini in the novel—and which is very different from celebrities today—is that he's not accepted by the upper classes. Back then performers weren't accepted as members of real society, even if they made a lot of money.
When he comes to pay his respects to a man hospitalized after an accident, he's humiliated when the family makes him leave. Because of this icy treatment, when he's invited to perform at rich people's homes he gets really uncomfortable.
In the book, Houdini is a vehicle for Doctorow to look at mortality. The death of Houdini's mother hits Houdini really hard, and he turns to spiritualism in order to hear his mother's dying words. Houdini attended séances dressed as an old woman, then "cast off his wig of waved gray hair and announced who he was" (40.21).
Holy mother issues, Batman: not only does Houdini try to connect with his mother in the afterlife, he even dresses up like her when he attends séances. Shades of Norman Bates?
Harry Houdini is also (like so many of the characters in Ragtime) symbolically significant. The dawn of the 20th century promised new and exciting magical escapes through scientific means: Want to fly? Try an airplane! Want to freeze time? Watch a movie! Harry Houdini personifies this new, bizarre-seeming technology by performing "magic" that is also based in scientific reality.