It depends on the downstream application, what do you need to do with it?

You may want to consider using Alpha Shapes (https://en.m.wikipedia.org/wiki/Alpha_shape) instead of a pure delaunay triangulation. Imagine you had a point cloud of a table, your proposed data augmentation would give you new points in empty spaces in the domain, which would ruin the original point cloud. Excluding points outside of the alpha shape would be a bit better. Even still, I'm not sure if this augmentation scheme is "valid" for most shapes, I think it would probably harm training if anything.