I don't think so.

The original question had to do with realizations of n-spheres in (n+1)-space. Specifically 2-spheres and 3-spheres in 3-space and 4-space.

When you say "gravity acts across 4D" I think you are referring to the description of gravitation n general relativity as the curvature of a 4-dimensional manifold. That manifold is somewhat different, even locally, from ordinary Euclidean 4-space. What is called the "metric" in GR is a smooth selection of a non-degenerate quadratic form for the formation of "inner products". But the form that is used is not positive-definite, which makes the geometry non-Euclidean, and the metric does not define a "metric" in the usual topological sense (since it is possible for distinct points to have zero "distance" in this metric). This rather scrambles the notion of a sphere, at least geometrically.

In contrast the question was posed in terms of Euclidean spaces, which come equipped with a positive-definite inner product, the ordinary dot product. This provides a simple way to realize a sphere -- just the set of ponts equidistant from a fixed point. Distance defined using a positive-definite quadratic form does meet the usual conditions for a metric in the sense of topology, and the geometry is what you would expect it to be.