I cut spirals like that when I move the carriage rapidly while not retracting the cutting tool. The trick is cutting a precision spiral. In order to do that, the lead screw has to somehow be synchronized with the spindle rotation. For threads, this is done through the gear train or with an electronic lead screw. The problem in cutting a fast , as stated earlier, is the pitch of the lead screw will require the lead screw to turn at a significantly higher rpm than than the spindle. This would be hard on the bearings in the gear box and for the lead screw. Obtaining a 8:1 or better increase in rpm would be difficult as well. For a lathe with a QCGB, it would have to be done with the external gear train. The largest pitch that your lathe can cut is 4 tpi so if you wanted to cut a 1 tpi helix, you would need to have an external 4:1 gear ratio between the the spindele and the input shaft to the gear box.
Assuming you were to do this in two stages and could split it more or less evenly, That would mean 2:1 on each stage. Your spindle gear has 48 teeth and if you drove the 120t gear, that would be a 3:1 reduction in speed. The second stage would need to provide a further 1.33 reduction or mor to be able to achieve thew overall 4:1 ratio. A further consideration would be the physical clearance. The sum of the number of teeth in the second stage will have to exceed 120 plus some in order to accomplish this. With the OEM gear set, you would probably have to use the 127t gear on the input shaft and one of the other gears on the banjo. You can the do fine adjustments using your QCGB.