Short answer: yes.
Long answer: I am by no means an elisp hacker, but looking at
TeX-command-region I thought that this could help:
(defun TeX-save-region ()
"Saves the TeX region to the file whose name is defined by TeX-region."
(and (or (null TeX-command-region-begin)
(TeX-pin-region (region-beginning) (region-end)))
(let ((begin (or TeX-command-region-begin (region-beginning)))
(end (or TeX-command-region-end (region-end))))
(TeX-region-create (TeX-region-file TeX-default-extension)
(buffer-substring begin end)
(Not that I exactly understand each and every part of this code, but the general idea should be more or less clear.) Now it remains to bind this to your favorite key.
Notice also that compiling with
C-c C-r does not "block" emacs, and in my setup I can hit
C-c C-r, continue editing the document, and as soon as the compilation finishes, the pdf viewer updates automatically.