Champion of Stormwind

Incorrect.

You need the "Exalted Champion of Stormwind" achievement, as shown above in the achievement series.

So, no, getting this achievement will not grant you the title.

to get the title of stormwind you need to complete the quest the valiants charge and the quest the valiants challenge and be exalted with them that will make you a "champion of stormwind" allowing you too ride the stormwind steed if your a different race your a race and then get the other titles for the achievment champion of the alliance.

These champion achievements aren't entirely obvious.

(1) In the main building, you need to complete the "The Valiant's Charge" for the particular faction. This will require 25 Valiant Seals. You can get these by doing the dailies @ The Argent Tournament Grounds.
The Valiant's Charge
(2) You will then get "The Valiant's Challenge".
The Valiant's Challenge
(3) Find Squire Danny (68,20):
[npc=33518]
*NOTE* - You must be on a jousting mount with the lance in slot. Otherwise Squire Danny will not give you the chance to fight.
(4) Argent Champion shows up and talks to Squire Danny.
(5) Battle Begins.
(6) Immediately "Charge" (3) champion. Activate "Defend" (4). Then keep at a distance and click "Shield Breaker" (2). I do the latter by just running away at an angle. Any time the Champion is at a distance, activate "Charge" (3) again. It's a very easy fight if you do this.
(7) Return to main building to cash in quest to get the achievement.

Note - This achievement takes a while because of the 25 Valiant Seals needed.