Why, yes.
Not really, not so neatly
-- or else they would have come up with a term (of their own invention, such as the word theotokus was invention amid Greek language) that would translate more precisely 'Mother of God' -- provided had that been the intent. Yet obviously, it was not?
They held back from going quite that far with the phrase (on purpose) yet without that slim margin of restraint equating to denying the divinity of Christ be inseparable from His humanity -- at least while the one known as Jesus Christ walked the earth (incarnate) in form of a man.
The same can be said for an alternative "phrase", or word ---Christotokus, which by itself denotes no inaccuracy.
Christ came to this earth in the flesh, in the form of a man, born of the virgin, Mary.
Jesus's very being in this earthly, physical realm was no spectre, not even the body (body of Jesus Christ) which resurrected from the grave, but instead was nothing but the real thing, baby, nothing but the real thing...
There are red herrings, in this world
and there are red cola cans.
Decide.
And what would "Mother of Jesus" tell anyone? That Mary gave birth to a son?
That would be remarkable to... no one.
The fact that Mary gave birth to the Second Person of the Trinity, in the Flesh of Jesus, is what makes the birth of Jesus remarkable. This is the significance of the title, "Mother of God." It points to the Incarnation.
Hoss