Yes, it is possible. Foreigner, who wishes to register a domain, is required to provide an extract or certificate of registration from the corresponding registry of the foreign country and/or other registry data requested by Estonian Internet Foundation for this purpose.
Estonian Internet Foundation, that administers TLD’s, has the right to demand that documents issued in a foreign country be legalised or certified with a certificate substituting for legalisation (apostil). EIF also has the right to demand the translation of the documents into Estonian. The translation must be performed by a sworn translator or the translator’s signature must be notarially certified.
NB! As of December 1st 2015 administrative contact of the .EE domain may be a natural person, regardless of nationality or residency.