I doubt it : Ricimer's political support was directly depending from the permanence of western imperialship : senatorial, especially in Italy, and military elites wanted an emperor in Ravenna at this point and really frowned upon Constantinople meddling with it.
There's a lot of reasons, some cultural and ideological (which ammounted more or less to "Roman Empire needs an emperor in Rome" and "those Greeks"), some social and political (notably the legitimacy necessities in province and the social progression depending on a relatively existing emperor).
Of course, there's little reasons to think Constantinople would agree and sanction Ricimer's tentative : IOTL they tolerated Odoacer's ambitions because it was only about an usurper ruler and Odoacer eventually acknowledge Nepos' claim if nominally only. Of course WRE as an independent polity is toasted at this point, IMO, but it was a bit too soon for people in the West to just acknowledge this, would it be only trough sheer inertia.