The two situations are different. In the first case the star is radiating energy in the form of electromagnetic waves. Actually it isn't a good approximation to think of the star radiating photons because the energy it radiates is delocalised. If you insist on treating it as photons you would have to describe it as a superposition of all the possible photon positions. This point is dealt with in more detail in the question Photons from stars--how do they fill in such large angular distances?. However it is certainly true that the interaction with the light from the distant star is periodic. Your CCD or photomultiplier tube would record intermittent signals not a continuous signal.
Anyhow, a mass like Earth, a star, a black hole or whatever is not continuously emitting gravitational energy in the way a star is emitting light - it is not continuously emitting gravitons.
If you treat gravity as a field theory, then the interaction between masses can be described by the exchange of virtual gravitons. However you should not take this literally as an exchange of particles like throwing tennis balls at each other. A virtual particle is just a mathematical way to describe a disturbance in a quantum field, and the interaction is built up from the sum of many such disturbances. The best article I've seen on this subject is from Matt Strassler's blog.
So there is no intermittent arrival of virtual gravitons, and no freedom from gravity in the time between their arrivals.