Yup, very few lenses actually support the 2.0x extender. And even those that do lose two stops of light.
So a 70-200 f/2.8 would be a 140-400 f/5.6.
Of the short list of lenses that support the 2x extender the majority lose AF as a result. Check the extender manual for approved lenses.
The 1.4x is much more kind regarding AF exclusion and only loses one stop of light.
If money is no object and you want 1200mm I would suggest
this lens.