the Helix is a parametric object (like the sphere/cube etc) which means you have settings to control the size/rotations etc in the object. All parametric objects can be made editable (top icon on the left bunch) Shortcut-C, that will make the helix into a spline object – no parametric controls anymore but it will have normal points like the spline you drew. Select your spline and the editable helix connect them and then you can close the gap between them.