I don't think so. Gravity is a property of matter energy, as is speed or mass. The gravity wouldn't change, I don't think, unless the actual amount of substance changed as that is the only way that would be to acquire more gravity.
However Gravity is electromagnetic in nature, as all things are said to be and operate according to the wave principle the forces can be manipulated quite easily and seem to operate chaotically given the sheer amount of data needed to interpret any given system. So conceivably, since gravity is a wave which is unique in terms of properties but also similar in terms of it being a wave then conceivably, I would think that any wave or electromagnetic energy could affect any other electromagnetic energy in any number of infinite ways.
If you think of space as a kind of bubble, rubber sheet, and/or membrane then large objects within that space would distort and effect the entirety of the rest of the space, like adding drops of water to a glass. The drops exists within the medium or "membrane" of a glass of water. The one drop affects the whole system.
If an object is rotating it is influencing the shape of it's container or medium and dragging it with it, much like your finger swirling the water around drags water with it as it does so.
So Yes I suppose. Idk lol, I just like talking about these things. Hope that help