|Many, many bulbs will multiply on their own, however, bulbs will have a hard time surviving, let alone naturalizing in an area that remains dry. The fact that grass has a hard time growing there means something more delicate (like daffodils, tulips, etc.) would also have a hard time. The sweet woodruff is suited to shade, and will withstand some dryness, but, will not thrive if the area is dry for extended periods. There are plenty of shade loving, drought tolerant perennials if you are interested in those. Many will spread over time as you envision. Consider: Alliums (one of the few drought tolerant bulbs), Alchemilla alpina, Arabis, Artemisia, Aruncus, Baptisia, Brunnera, Epimedium, Helleborus, Hemerocallis, Hosta, Lamium, Penstemon, Sedums, Tovara, Nepeta, and Antennaria. You can improve your chances of success by improving the soil in your planting area by working some organic matter such as compost, leaf mould or composted cow manure into the site. If you could till it into the ground in thespring, that would be great.