No, the use of a domain name alone does not create any rights to the domain as a mark.
So non use would certainly not generate any rights in ecomedy as a mark - but thats the point.
It would be descriptive and non distinctive, any markholder would likely only be granted rights in it in a non descriptive capacity - e.g. ecomedy could be a made of cereal, a beer or a car.
Trademarks do not prevent blanket uses of a term:
"A trademark does not confer a right to prohibit the use of the word or wordsââ¬Â¦. A trademark only gives the right to prohibit the use of it so far as to protect the owner's goodwill against the sale of another's product as his." Prestonettes, Inc. v. Coty, 264 U.S. 359 (1924).
Trademark scope is evaluated based on a sliding scale of distinctiveness, so ecomedy would be weakly protected within the scope of any mark registration even if the domain registration came after the trademark registration.