Check it out for your self:
The Y travel is 12 inches.
Measure the distance inside the MiniMill enclosure from the inside of the door to the Z way covers at the back; this is measurement M.
Measure the overall length of the vise from the end of the screw to the back end of the moving jaw when the vise is fully open; this is measurement V.
If M minus V is smaller than 12 inches you cannot mount the vise without it hitting either the door when the machine is at Y0. or the way covers when it is at Y-12.0.
If M minus V is larger than 12 inches you are okay.
However, if M minus V is something like 10 or 11 inches and you are machining small parts it may be possible to mount the 4" doublelock and use it safely by reducing the maximum Y travel to 10 inches. This will only work if you still have enough travel to reach all around your parts.
An open mind is a virtue...so long as all the common sense has not leaked out.