The official upgrade strategy for Linux Mint has been explained here by Clem: How to upgrade to a newer release
. Clem's answer to your question consequently would be: no, you cannot use the Mint Updater in order to perform a distribution upgrade.
There is, however, a way of imitating the Ubuntu behaviour by following this tutorial: Upgrade linux mint in-place using apt
. I.e. you canot use Mint Updater, but you can use apt
commands (commandline) or Synaptic
(GUI) in order to achieve your goal.
I do wonder, however, whether replacing Linux Mint 13, a stable release which will be supported until April 2017, by a short lived interim version like Mint 14, which at this point in time only exists as a release candidate, is a wise idea at all. - Yet, this is your decision.