If I sleep on my stomach with large breast implants, can that deform my ribs?

I do not think lying on your implants will cause a rib deformity and decrease your vital capacity to breathe.  

This would be quite unusual. I have seen mild rib indentation/contour changes from long standing, tight tissue expanders. Any changes in rib contour are unlikely to have any significant effect on your lung capacity.

I know of no evidence nor have I seen this happen with patients sleeping on their stomach with implants. I have observed flattening of the ribs when under a tissue expander but even this is relatively minor and not visible through the skin. Hope that this answer helps.