The Sangharaj holds authority over all monks ordained in the Thai sangha, whether inside or outside of Thailand.  For example, it is through the Sangha council that monks are authorized to perform ordinations and through which the title of 'Somdet' is awarded.  However, the two monasteries you mention are slightly different from most Thai wats you find outside of Thailand.  Most Thai wats, for example here in San Francisco, are closely associated with the Sangha council which is heavily involved in the wat's operation.  (I think)

Amaravati and Abhayagiri pretty different because they are 'forest monasteries' and also because they are for Westerners.  Most forest monasteries tend to be fairly uninvolved with the formal Sangha administration, and doubly so the Westerners.  The various branches of Wat Nanachat tend to do their own thing, but still are bound by the Thai Sangha in certain ways.  For example, only Ajahns Sumedho and Pasanno are authorized by the Sangharaj to perform ordinations, so all ordinations within the branches of Wat Nanachat in the West are done by one of those two, whether here in America or in Australia, etc.