Is there any adhesive property to the sand encouraging stability of pavers?

Not really. Unless you align the pavers so the space between the pavers are not all in a straight line, rain will wash the sand out. Also, until the pavers have settled well, say in a year or two, you might want to drive short wood stakes, flush with the tops (window molding or scribe, cut to about 6" with a cut point on one end.) against the exposed edges of the paver. Once grass has been established around the perimeter, the pavers should stay in place. You may have to re-sand the cracks one more time.