The accumulator controls the hydraulic pressure on the apply side of the kickdown servo during the
1-2 shift. It provides cushioning for the kickdown band application at any throttle position. The spring affects the cushioning.
Some shift kits, or aftermarket valve bodies, specify leaving the spring out, or leaving it out plus adding a blocker rod to increase 1-2 shift firmness. The spring is sometimes just left out by itself hoping to increase 1-2 shift firmness. It might affect the firmness in some cases, but can affect engagement harshness into gear.
There is debate on whether its absence is beneficial or harmful in a stock transmission. I typically install them if the transmission is stock or follow what the shift kit specifies in those I build with a kit. For shift kits, I use Trans-Go or older Fairbanks kits.