If the planet and satellite are perfect spheres, or any convex shape then the answer is NO. If the planet is close to the satellite and you stand on the point nearest to it then you will only be able to see a small band around the horizon, but the whole horizon cannot be blocked.
If the satellite is not convex and you stand in a hole or crater on the satellite so that your view of the sky is reduced then the planet can fill the rest of the visible sky, so the answer is YES.
If the satellite itself is a sphere then the planet cannot obscure the whole horizon unless the satellite somehow passes through a tunnel or at least a gorge in the planet, not very likely
Update: Since the question has been updated there are a couple of extra points to be made
If the observer on the satellite is limited by the resolution of his vision then a sufficiently big planet could obscure the whole sky with the only band of sky left near the horizon being too small for him to see.
Also, regarding Carl's comment on the effect of GR. If the planet is sufficiently massive, but not the satellite, then light will bend towards the centre of the planet. In this case it is possible for the planet to cover the whole sky in the most extreme circumstances.
As mentioned in the comments on this answer, an atmosphere on the satellite would bend the light towards the satellite making it harder for a plenet to cover the whole sky.
If the atmosphere is on the planet it could only help if the satellite was inside the atmosphere, in which case the drag would slow it down so that it would not remain in orbit for very long.