Had a further couple thoughts on this topic.
1. The Imperium doesn't need to crush the Vargr and in any event IMO cannot due to their tribal raider/decentralized nature.
The Imperium does need to worry about the Solomani, the Zhodani, and those nuke wielding herds, and so minimal resource/maximum effect would be the watchword.
So playing packs against each other, supporting one then the other, ensuring one pack never 'unites the clans' like classic British divide and conquer would be the way to go.
2. Since sophonts will tend to look at others through their own cultural lens, the Imperium would look like a SuperPack to Vargr.
And all that pledging fealty and nobility, etc. would likely be interpreted as meaning the Emperor was a megacharismatic figure of epic proportions.
In that instance the Emperor may loom larger to the Vargr then to his subjects and vassals.
As such, a simple note from the Emperor, positive negative or even diplomatically, may be worth fleets in the hands of an adept Archduke.
Conversely, if the Emperor is assassinated, civil war starts or even just a low level succession crisis erupts, the perceived 'charisma' of the Emperor and his Imperial MegaPack can wane in Vargr eyes and cause more pack leaders to chance bold action.
3. On the point of how the Vargr could be threats, if one thinks of them as steppe raiders, such peoples have produced military leaders like Genghis Khan and Timur, could be some real talent develops with all that pack struggle.