No,it does not make sense.
In General Relativity, gravity does not effect space, rather gravity IS due to the curvature of space-time, and the degree of space-time curvature is depends upon the mass-energy located at a point in space.
So in a Newtonian framework, we view gravity as a force field generated by the presence of mass. This force field we perceive as extending through space, but not effecting space. However, when we move to the more accurate General Relativity framework, wear space-time is "elastic", we find that the presence of mass (or more generally mass-energy since mass and energy are equivalent within a relativistic framework), warps space-time, and it is this warping or curvature of space-time is what we perceive to be the gravitational field. This is why in Newtonian physics the bending of light around massive bodies is not predicted (i.e. Newtonian physics tells us that light will only ever move in a straight line, since a beam of light has no mass, and so is not effected by a gravitational field), but it is a consequence of general relativity, since the light is simply moving "straight" through curved space-time, and hence appears to our senses as being bent by gravity.
This is all well and good in General relativity, when objects are large and massive, but on the quantum scale general relativity breaks down (both philosophically and mathematically), which is why we have not yet a fully coherent theory of quantum gravity. It is thought that gravity on the quantum scale is mediated by gravitons, which are the quantised particle of the gravitational field (just as photons are the quantised particle of the electromagnetic field). Thus, since gravity is curvature of space-time, gravitons should be the quantised perturbations of curved space-time. In general relativity, the interaction of massive bodies produce gravitational waves (which again is a macroscopic perturbation, or oscillation of curved space-time), and just as electromagnetic waves can be considered as an ensemble of very many photons, a gravity wave can be considered similarly as an ensemble of very many gravitons.