Not even the Breen sector is locked out. You can access the sector any time. It's actually just the Borg and Undine sectors you have to be RA3 for.
You won't be able to access the missions there until you are sufficiently leveld up though.
I would imagine, forced mission progression or not, that a new Feaure Series will be level agnostic and maybe unlocked with a minimum of LC1 or so.
However, Cryptic might decide to hold the mission back a little further once FTP is released so all those new players have an actual chance to be high enough in the usual release weeks to get the special rewards.
So expect the mission a month after FTP at the earliest.
If we are lucky they rerun the other 3 (has it only been 3) before that.