In OTL the closest we can get to this scenario is
Zeno the Isaurian.
But the Isaurians had been living inside the Roman Empire about five hundred years and they had been Orthodox Christians since the very beginning for centuries. And even that did not make these people too "Roman" by the "true Romans" - the Isaurian army detachments got occasionally slaughtered by the Roman mobs and other imperial troops and things like that.
So if you want a Norse/Anglo-Saxon guy repeat the success of Zeno the Isaurian... first thing - make the group of the Norse settle inside the Roman Empire, adopt Orthodox Christianity and live there for 500 years or so. And then let this guy try to pull Zeno the Isaurian.
...and ye, pray hard for him not get killed and dethroned in the process for his un-Romanity.
You see, the reason for these Norse and Anglo-Saxon guys got hired as the Emperor's guard was not only their exceptional martial qualities. The other reason for bringing guys from a thousand miles distance was - any one of them had zero chance to dream of the imperial purple no matter what, and they never worried about supporting their tribesman to reach the throne, as they did not have any to support. Which made an emperor feeling somewhat more comfortable having them around.