(last updated: 12/30/17)While the BlazBlue cast has been largely integrated as described on the BlazBlue notes page, there are a few additional challenges with the series that bear pointing out specifically.
The following characters, while playable in the game, are not available for application as separate entities as they are fundamental aspects of existing characters:
Izayoi - Included as an alternate mode for Tsubaki
Mu-12 - Included as an alternate mode for Noel
Susano-o - Included as an alternate mode for Terumi
Hazama - Included as an alternate mode for Terumi
Although Hakumen is Jin Kisaragi from another timeline, he is a separate enough character conceptually that both Hakumen and Jin Kisaragi are available to be played.
Also, the various 'dolls' in the cast are aspects of the characters they fight alongside and cannot be applied for as separate characters:
Ignis - Part of Relius's character
Nirvana - Part of Carl's character
Minerva - Part of Celica's character
In addition, a special point should be made regarding BlazBlue Centralfiction. The majority of the narrative in this game takes place in an alternate existence (The Embryo). In this existence, many of the characters are experiencing memory loss or jumbled memories, significantly altered histories, and even some personality shifts. This note is just to caution that using CentralFiction as a basis for character backstory or personality notes can be very misleading.
That isn't to say that there isn't any useful canon information from the CF narrative. Some characters experience no memory loss or changes to their history, and there are also many flashbacks and elaborations on events prior to the point where everyone ends up in The Embryo that can be very useful sources of information. It's just that understanding what is or isn't safe to draw on as a reference requires a lot of analysis and a comprehensive understanding of the entire BlazBlue story.
If you need any help in figuring out what is legitimate or not for the BlazBlue cast on MotM, please reach out to Wheatley or GLaDOS to discuss it.