Simultaneous control is possible if you have a 4-axis control.
You use G01 only, with all four axis distances/angle.
Feedrate of rotary axis ("A" is parallel to X, "B" parallel to Y and "C" parallel to Z. So, you have A-axis on your machine) is in deg/min, if commanded separately.
If you use a linear axis as well as a rotary axis in G01 (as in your case), the commanded feedrate would be along the tangential direction of tool movement, i.e., along the spiral toolpath.
This way you can generate a uniform pitch. If you need a complex contour, defined by lines/arcs, on the circumference, you need to have cylindrical interpolation available on your machine.