Is the double dollar sign ($$) quotation method in SQL standard?
NO  its postgresql specific many programing languages offer a way to write text that avoids having to be escaped 

consider

Select $$";"'\e\r\n$$ 


vs

select '\";\"\'\\e\\r\\n'


Also keep in mind Postgtesql from version 9.1 by default no longer allows passing escape string in a query,  it has to have a leading E   

select E'\r\n'  


to be escaped now 
see standard conforming string