C-c C-a uses AuCTeX's heuristics for deciding which list of commands to run. The usual case is to use the function TeX-command-default which is defined in tex-buf.el. So no, latexmk is not used.
You can make latexmk accessible from C-c C-c by customizing TeX-command-list. One possibility is to a add an element of the form
INS DEL :
Name: LaTeXmk
Command: latexmk %s
How: Value Menu TeX-run-TeX
Create a process for NAME using COMMAND to format FILE with TeX.
Prompt: Toggle off (nil)
Modes: Value Menu All
Menu elements:
INS DEL Lisp expression: :help
INS DEL Lisp expression: "Run latexmk."
INS
which adds
("LaTeXmk" "latexmk %s" TeX-run-TeX nil t :help "Run latexmk.")
to TeX-command-list. Once this is done, on typing C-c C-c you can choose LaTeXmk as the command to run. Next time you type C-c C-c this will be offered as the default, so can be accepted with just RET.
Look at the other elements in TeX-command-list to get an idea of ways to pass further options to latexmk should you need them.