shallow arcs - large radius - milling machine limits

The project is to mill a shallow arc in a shorter piece of aluminum The aluminum blank is 4 inches long by 2 inches wide. For this question lets say the mill bed has an 8x8 movement range. Let's assume the blank is mounted to allow the bed to cover the entire blank My question is will CNC limits allow cutting an arc with a radius 12 inches from the blank?
The core of the question is: will LinuxCNC allow a reference that is beyond the bed limits ?

The toolpath matters. As long it is within machine limits, you can machine any contour or radius.