I've implemented this in my Line-Drawing Game Starterkit and avoided using the over-engineered solutions. You probably need a point every 10 pixels distance, so you can get a decently smooth line without using too much memory or draw calls. Then it's a simple matter of moving the objects from point A to B. To make them appear as traveling smoothly along the path, you simply rotate them to the direction of motion. This is done over time and not instantly, so you get smooth, following a curved line movement without the need to used Bezier curves or similar.
The points are stored in a simple array, inside a Path class that also knows how to draw the path using OpenGL. You can have any number of path points but I would limit them to 50 to 300 depending on the device and required smoothness.
To interpolate the line you should look up the McMaster's Slide Averaging Algorithm (theory).
The object is moving to the first point only when the user has drawn at least two points, to avoid the object spinning wildly. Once moving towards the first point its the same code as moving to the second, third, fourth and so on.