The stump being removed will not prevent the root suckers from growing because the roots still have energy storage and are sending up the tree shoots as a stress response to the main tree being cut down. It could take a number of years for the roots to lose their source of energy but if you keep cutting the shoots down or carefully apply a systemic herbicide that can help with the maintenance. You could have the stump ground and the main roots ground out which could cut down on the amount of shoots you are getting but you would probably still have some from other roots in the area depending on how large the tree was and how far the roots extended. 

It isn't proven that drilling holes in the stump and adding salt is an effective way to have the stump decompose more quickly. You just need time. Potentially if you drill holes and keep applying water to the holes the water could help it rot faster. Or if the stump is in an area that could be a focal point for a garden, you could apply some mulch or wood chips around it to create a garden! 

Let us know if you have further questions or would like more guidance on a garden area.

Emily