Behaving differently depending on where point is in the line is the easy bit (see (if (looking-back "^") ...) in the code). "[Working] as a tab normally would" is the harder bit, as that's contextual.
Here's one approach, but I was thinking afterwards that a more robust method would be to define a minor mode with its own binding for TAB and let that function look up the fallback binding dynamically. I wasn't sure how to do that last bit, but there's a solution right here:
Emacs key binding fallback
(defvar my-major-mode-tab-function-alist nil)
(defmacro make-my-tab-function ()
"Return a major mode-specific function suitable for binding to TAB.
Performs the original TAB behaviour when point is at the beginning of
a line, and moves point to the end of the line otherwise."
;; If we have already defined a custom function for this mode,
;; return that (otherwise that would be our fall-back function).
(or (cdr (assq major-mode my-major-mode-tab-function-alist))
;; Otherwise find the current binding for this mode, and
;; specify it as the fall-back for our custom function.
(let ((original-tab-function (key-binding (kbd "TAB") t)))
`(let ((new-tab-function
(lambda ()
(interactive)
(if (looking-back "^") ;; point is at bol
(,original-tab-function)
(move-end-of-line nil)))))
(add-to-list 'my-major-mode-tab-function-alist
(cons ',major-mode new-tab-function))
new-tab-function))))
(add-hook
'java-mode-hook
(lambda () (local-set-key (kbd "TAB") (make-my-tab-function)))
t) ;; Append, so that we run after the other hooks.
