Quote Originally Posted by Averax View Post
Assuming they're opting for cohesion, it'll probably take place after the 1-50 MSQ and before the patch content.
I think the recent digest for the Last Live Letter actually answers this to a degree. For new Players going through the story, once they finish the quests in 2.55, they will get a notification to complete the Crystal Tower story if they have not already. It was not specified if players would be blocked from entering Heavensward, or that block would be in place for only 5.3 quests, but with the way it is worded I believe it is in fact the latter.

Quote Originally Posted by Zhexos
Before you begin the Patch 5.3 main scenario quests, you’ll need to have completed the Crystal Tower quest series and “My Little Chocobo” quest. With the Crystal Tower series’ relevance to the main scenario, we decided to make it a requirement.

Players will be notified of these progression requirements at certain points during the main scenario. For instance, if you recently started FFXIV and are progressing through A Realm Reborn, a popup asking you to complete the Crystal Tower quests will be displayed before you begin the Heavensward main scenario.