Sr2+ is similar enough in properties to calcium that it can replace calcium structurally (if not entirely functionally) in those enzyme systems that utilize calcium as a substrate. Radioactive strontium was at one time considered as a potential fuel for some nuclear reactors until it was determined that the human body readily makes bone out of it, and thus plant workers who were exposed to even small amounts would have a greatly increased mortality. As far as I know, humans do not require Sr to make bone, and thus deposition is by biochemical accident/mass action.
In all likelihood coral enzymes have as much trouble distinguishing between Sr2+ and Ca2+ and thus there is deposition of both based upon local concentrations of each (mass action). So in other words, if you dose Sr, your corals will have Sr in their skeletons. If you don't, they won't. Whether SrCO3 adds structural stability (and therefore increases growth rate) of coral skeletons is a question for the structural geochemists/inorganic crystallographers to answer (and the answer is probably no).
Personally, I don't think it's worth the effort. I haven't seen significant changes whether I dose Sr or not.