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.
2nd edit: As far as I know, the slice-ribbon conjecture has no real consequences. As I describe above, it's more of an ''outer-marker'' type of conjecture. It's a measure of how well we understand knotting of 2-dimensional things in 4-dimensional things.