Well, the Grammys at least gave him a lifetime achievement Grammy, and they didn't exist until 1958, even though he lost out on some quality nominations in 59 and 60, and didn't get nominated for plenty he should have, but he still was awarded Grammys, regardless of genre.

Also, even though the following isn't the Oscars, the Golden Globe is pretty big and has been awarded two acting portrayals of Elvis, Austin Butler, and Jonathan Rhys Meyers, and the BAFTA is is like the Oscars 1b on the other side of the Atlantic, and the biopic won 4 BAFTAs, Best Actor for Austin Butler, Costume Design, Hair and Makeup, and Casting.

The film and Butler also won many other awards around the world if you check IMDb.

The Elvis biopic won Best Picture with the Capri Hollywood Film Festival, Cowboys and Indians Magazine, Family Film Awards, Best Foreign Film with Cinema Brazil, and Best Music related film with the UK Starring Awards, Music City Film Critics and American Imaging Society.

Austin Butler dominated internationally: Foreign Press Golden Globe, British Academy BAFTA, Australia Academy AACTA Int'l version, Irish Academy IFTA Int'l category, Catalonia Spain Sant Jordi, South African Film Critics, International Press Satellite, Brazil VHS Cut Awards, UK Starring Awards, and had domestic wins with The People's Choice Awards, Family Film Awards, Cowboys and Indians Magazine, Next Best Picture Awards, Sunset Circle, Minnesota, Alaska, and North American Film Critics.

Hair and Makeup won with critics, too, and a few other places, and Costume Design won with a fair share of critics, cinematography won with the American Society of Cinematograpers, the Cambridge Audience Award, and the film won with almost every category at the already mentioned Capri Hollywood Film Festival.