That's some big, aggressive fish - and heavy stocking - for a 240. Some of those fish will outgrow a 240, and some are just too much aggression and bioload, when combined, for the tank.
I know you just asked about adding the annularis, so if you don't want any advice beyond that, skip my post.
There are tanks the size of yours with a large number of aggressive fish. But even danorth's tank (which is a success, and an exception) is not as heavily stocked as your list.
Here's a list (from your list) of what I'd keep in that tank and what I'd eliminate.
Angels - I don't think I'd keep more than three in this tank.
-Blue Face Angel - keep (but they do get big)
-Emp. Angel - keep (they get big)
-Annularis - keep (not the most aggressive, okay size)
-Blue Angel - no - too many angels, large size, potential aggression (Holocanthus is the most aggressive genus)
Triggers - substitute smaller/less aggressive, limit to two
Clown Trigger - no - too likely to get aggressive and outgrow tank
Picasso Trigger - fine
Niger Trigger - may be okay, but gets really big
Tangs - the unicorn and vlamingi tangs you selected get way too big, choose some other tangs, limit to no more than three, try different genera.
-Unicorn Tang - no
-Vlamingi Tang - no
-Yellow Tang - OK size, nice coor, not one of my favorite tangs
EDIT: I just noticed another post of yours and see you already have many of these fish. I'd avoid adding the annularis based on the stocking you have already. I think you probably are going to have continuing aggression challenges with the fish you have, even in the bigger tank. I'd just get the fish you have into the 240, and let things settle down before adding any more. JMO.
