This can be done, but you have to really want to. You will need to model the threads on your screw with a helical sweep. In the nut, you don't need the threads. Instead, make a sketch with a point located in the middle of the thread flank. Mate this point to the helical face on the screw. Once the nut is mated to prevent rotation, it should move along the screw when the screw is turned.
This model will take a long time to rebuild because of the helical sweep. You may not even be able to make the helical sweep long enough without running into problems. Different versions of SW have been more or less capable with this, so you'll have to try and see. If you don't need to show the helical threads in the solid, you might try using a helical surface instead. The surface should rebuild faster.