I think contamination is the only issue. Since you're not worried about that I guess it doesn't matter.
The Fuji bleach and fix I use is supposed to be
Tank #1 bleach
Tank #2 a mix of bleach and fix
Tank #3 is fix
Tanks 1 and 3 over flow into tank #2.
I use a wash in place of tank #2 but I'm reusing my bleach and fix.