I don't know a genuine link to the smooth Poincare conjecture but the link to cobordism for homology spheres is simple.  Given a slice disc, construct a branched cover of $D^4$, branched over the slice disc.   That gives you a 4-manifold bounding the associated branched cover of the knot in $S^3$.  I wouldn't describe it as an approach to determining which homology 3-spheres bound homology 4-balls but it's a natural source of examples, and a linkage. If anything the information seems to flow mostly the other direction.  For example, Paolo Lisca's recent paper where he determines precisely which connect-sums of lens spaces bound rational homology balls.  As a corollary he deduces the order of 2-bridge knots in the concordance group of knots in $S^3$. 

EDIT: Not exactly addressing your question, I think of the slice-ribbon conjecture as a primitive 4-dimensional knotting problem.  Given a slice disc you could ask if it's isotopic to a ribbon disc (if the height function on $D^4$ when restricted to the slice disc has only 1-handle and 2-handle attachments, in that order).  You can mess up a ribbon disc by taking connect-sums with 2-knots.  So modulo connect sums with 2-knots is every slice disc isotopic to a ribbon disc?   Perhaps that's too much to ask too, so you can ask the slice-ribbon problem.