You could sweep a corkscrew surface toward the inside of the helix, and then get the curve at the intersection of the surface and solid. The continuous issue is something you may be able to deal with downstream.
I use ST5 cause my school hasn't gotten an upgrade yet, but if you try using the wrap sketch command which can be found in the ordered section of Surfacing, you should be able to do this no problem.
First create a plan that is parallel to the bottom of a face on your pyramid.
Second, creat a line at which ever angle you want the pitch of the helix to be. then make a straight line. as far as you want the sketch to wrap. if you want it to the top, you will ne to make sure the line is even with the top of you part.
And last, just use the Wrap Sketch command on that line, and that part. it should just wrap it right around and have it all on the face.