If by “staggering” you’re referring to the slightly different string lengths (longer for the lower strings), then my answer is No, it’s not strictly essential, but still recommended. The physics of string intonation apply whether the instrument has frets or not. Thicker strings are less flexible at their termini than thinner ones. And while a fretless instrument can theoretically be perfectly in tune for all notes, not intonating the strings means your fingering positions would necessarily be in slightly different positions for the different strings. Single string bridges should have some adjustment built in though. So even if the actual bridges aren’t staggered, you should still have some room to move their saddles fore and aft. Whether there is enough range of motion is the question. In practical terms, for a fretless instrument, especially one with a scale length as long as this one, approximate is good enough. So if the bridges have enough adjustability to make each string approximately its width’s amount longer than its neighbor, you’ll be fine. If not, then I would recommend staggering them.