Hi,
Post the datasheet, not the shop page
. If the PSU has to sense a load of parallel strings, surely it would need multiple constant current sources to sense each string, or the designer would need to do a very delicate balancing act to match the load on every string, presumably bearing in mind temperature effects and more, a bit of a Swiss watch-maker's task, and I suspect not wholly realistic. While I'm sure you could get away with it, and hopefully no string would win the current-hogging race and get all greedy and frazzle, it sounds like a dodgy method I would not employ myself for any serious project.
There are plenty of LED driver ICs which can monitor from a few to many strings, with protection circuitry included, I'd have gone that way myself - one whatever is big enough power supply and a few LED driver ICs, but still.