Not exactly. First, standbys and non-rev's will be told "no go". The first to be bumped will be those who show up late and those without seat assignments. Then they will move their ticket holders with the highest FF status to first to free up coach space. If they still need room they will move those who have paid the most for their tickets to first.
As long as you have seat assignments you should be fine.
Remember, what you see online isn't the real peicture. The mid plane exit door seats will always show as sold out, but aren't. Also the first 3-4 rows in coach might be showing as sold out but aren't, they are reserved for the highest FF status fliers and disabled people.
To increase your chances, get to the airport early, like 90 minutes or more early.
Anne