There is an easier way, actually. I just tried it and it worked.
A cylinder connection makes 2 degrees of freedom: one rotational joint axis and one translational joint axis.
You can get the same effect as the nut threading on by creating a gear connection between the two joint axes created by the cylinder connection. The gear connection is a Rack and Pinion type connection, however.
Assemble the nut onto the screw using a cylinder connection (when you assemble it, press the "Connect" tab at the top of the assembly dialog).
Go into Mechanism mode, and create a gear connection using Mechanism-->Gears.
Change the type to Rack and Pinion, and pick on the joint axis icon between the nut and screw for both the rack and pinion settings. It will automatically choose the correct one for each. Under the Pinion tab, you have to enter the pitch circle diameter. Since it thinks this is a rack and pinion, it will translate the rack axis by:
3.142*Pitch_Circle_Dia (for every full turn of the pinion)
So, work backwards and take the pitch of your screw and divide it by 3.142 to get the pitch circle diameter to use.
i.e.) For a M8x1 thread, the pitch circle diameter is:
Dp = 1 mm / 3.142
= 0.318 mm
It sounds more complicated but its actually much easier since you don't need thread geometry or helical curves.