[Answer added for completeness.]
⎈ CtrlR initiates a loop cut and a new edge loop intersecting the chosen edge.
To cut through a number of edges, which are not connected by edge loops, use the Knife Tool.
- Go to an orthographic view (front view).
- Press K to enter the knife tool, press Z (to enter cut through mode) and C (to constrain the angle). Then draw a poly line with two LMB clicks. Press ⏎ Enter to confirm.
The options you activate while the tool is selected.
Cut through Z
Allow the Cut tool to cut through to obscured faces, instead of only the visible ones.
Angle constrain C
Constrains the cut to 45 degree increments.
It's impossible because the loop cut tool is based on your topology, it basically creates one or more loops inside a loop.
However, what you can do is to use the Knife tool with K, if you watch the 3D viewport's header you will see the Knife tool's options. including the "cut through" Z which, once enabled via its shortkey Z, will allow you to cut a straight line through the mesh. Just set a side/front view and that will do the job.