Cohorts are built as characters, but they aren't built by the player.
The DM determines the details of the cohort. - DMG p106
All of the text that talks about how cohorts are made, and how their level is determined, and how they advance uses the term "level" to talk about cohort power. This strongly indicates to me that cohorts are supposed to be built just like characters are, and advance like characters do.
This means that if you build a character using a monster race, then it likely will have an LA, and thus have less character levels than it otherwise would. Also, the rules say that while you can "try" to get a cohort of a particular race and class, it's ultimately up to the DM what you actually get.
For a blue dragon specifically, there is a table on page 139 of the Draconomicon that says what ECL each dragon is for the purposes of Leadership. You can get a Young Blue Dragon as an ECL 17 cohort, which should tell you just how screwed up the ECL system is. Realistically, you can't get an effective dragon cohort outside of very early levels. Once you get a dragon cohort, it will advance as a character, until it's old enough to advance an age category, and then have its HD and ECL increase, likely to a point beyond what you can have as a cohort.