I think there is potentially more trouble than just this in the spell. The hound only attacks hostile creatures within 5' of the caster. You may literally have to stand next to it and, dm ruling dependent, it may not be able to attack things on the opposite side of you. Anything with reach can be immune to it's attacks by simply not being adjacent to the caster.
In addition since the hound can't take the hide action the common interpretation of stealth says that everyone knows there's an invisible thing in that space.