The reason why I put the emulator last is because back in the day of big consoles, the kind of effects put in the ProChannel (like compression and EQ) were either before the mix bus, or channel inserts that were also before the mix bus.
However...remember there are two components to console emulation, transformer emulation and non-linearities. Non-linearities will have the most overall effect if at the end. Transformer emulation is something else, depending on whether you want to have a transformer at the input whose character then gets processed, or at the end, where the "clean" signal gets character.
One of my favorite Console Emulation tricks is using it as an effect on bass by turning the drive way up and "saturating" the "transformer." The primary transformer distortions and character happen in the bass range, so it's a natural for processing bass (including synth bass). For this, you want it at the beginning.
So as has been said many times, where to put the Console Emulator is a matter of personal taste. But the more clearly you understand how it works, the easier it is to apply in an appropriate manner.