No, you'd have to replace the spring (which doesn't look possible on the stock shock... it appears to be friction welded or something at the top where you would normally unthread the top eyelet to remove the spring... could be wrong though), but then the dampening on the shock would probably be too aggressive for the softer spring rate, which would be far worse feeling than just leaving the stock shock alone. Ideally you'd have a dampening adjustable rear shock that you could change springs on, and adjust the dampening on accordingly to match the new spring rate and how you want the bike to react over bumps.
The only other thing you could do, is affect the leverage point of the rear suspension to be able to apply more leverage to the shock, thereby requiring less weight to compress/work the shock package... then it would 'seem' to be softer... however with the stock rear shock, there's no room for that, without significantly increasing the ride height... and if you put the shock in a location where it WOULD be possible, the leverage point would be moved so far, you'd actually need a stiffer shock to get the proper softer feeling...
Has anyone ever found a shock from another bike that could fit a Grom? I was thinking maybe from a cbr or gsxr might work. If that was the case we could just buy a used cheap one off eBay. Those shocks are usually adjustable and much higher quality than whats no it now
PS it would be great if someone could tell me the size of the hole for the 2 bolts holding it in. I'm willing to do research and find out if there is anything out there that could fit.