If you are referring to cbanims, talking head animations, weapon/ship anims, and the like then no, it can't and won't use EFF. I'm working on a new animation format specifically for those purposes (something smaller in file size and better suited to streaming). The format for EFFs was setup specifically for effects and it's not possible to stream them. The new format will be just for interface animations, uses JPG images for frames, and has the entire animation as one file (like ANI does now).
For most other things (hud graphics, some buttons and things, etc.) it should be able to use either ANI or EFF already. The only problem with that at the moment (as I look at the code) is that you would have to put the EFFs in either data/maps or data/effects for them to load. I never added EFFs to the file cache filter for data/hud or data/interface, but I'll take care of that for 3.6.9.
