Yes, Mach3 perfectly understands 3-dimensional arcs. Here is an example of a hole cut in spiral motion:
G0 X-11.5 Y0.0
G3 X-5.75 Y-9.9593 Z-0.1667 I11.5 J0.0
G3 X11.5 Y0.0 Z-0.5 I5.75 J9.9593
G3 X-5.75 Y9.9593 Z-0.8333 I-11.5 J0.0
G3 X-11.5 Y0.0 Z-1.0 I5.75 J-9.9593
G3 X-5.75 Y-9.9593 Z-1.1667 I11.5 J0.0
G3 X11.5 Y0.0 Z-1.5 I5.75 J9.9593
G3 X-5.75 Y9.9593 Z-1.8333 I-11.5 J0.0
G3 X-11.5 Y0.0 Z-2.0 I5.75 J-9.9593
G3 X-5.75 Y-9.9593 I11.5 J0.0
G3 X11.5 Y0.0 I5.75 J9.9593
G3 X-5.75 Y9.9593 I-11.5 J0.0
G3 X-11.5 Y0.0 I5.75 J-9.9593
G0 Z0.0
What CAM program are you using?