According to the Batman Annual that featured Jason's OYL "origin" he did exactly that after he left Talia and Ra's and the Lazarus Pit, following Bruce's training path through Asia but deliberately not using the same teachers. That's where/when he adopted the kris as his signature blade.

But yeah, I wouldn't mind having current-Jason stop Batting around to just "walk the earth" like Kane in Kung Fu for a while.