No, there's a great deal of theory involved in jazz. You need to be able to instantly play any chord (and jazz uses only chords of the seventh or higher, not major/minor triads), in any inversion, in any key, instantly. That's just for basic pre-1960 style. After that you get modes and God knows what all.
These days there aren't many professional jazz musicians who haven't been to a good music school. A lot of conservatories and top university departments teach it, and there are other schools just for jazz.
For learning jazz piano at home, I still recommend the series by John Mehegan (4 volumes), although obviously it's pretty old by now. But he's very thorough and there's lots of examples.
There are also books of transcriptions of solos by famous artists, like Monk and Bud Powell etc. These are fun to play but maybe not the best way to learn to improvise. (Not to mention really old stuff like Jelly Roll Morton.)