No, the Imperium is spread throughout the galaxy. That doesn't mean it owns all of that space. It's not like ancient empires on Earth where you almost always had borders which expanded outward and everything within them was yours. (I know this wasn't always the case, but it was in the majority.)
There are a massive amount of other races and factions spread throughout the galaxy all occupying parts of it (the Tau are just a fairly prominent example of this), they just aren't displayed on all of the maps of the galaxy because that would take ages to do. Despite what Ward would have you believe, the point in 40k is that the Imperium of Man is assailed on all sides, inside and out by all manner of aliens and heretics, and they fight their hardest to hold out in the sectors of the galaxy which they do own.