Bed size vs Camera angle lens options

Your math looks right, yes.

If you’re going for “basic alignment” that should work, but if you want good accuracy on the sides with a bed of that size, I’d suggest going with a 120 degree lens to minimize the distortion. A 160 degree lens means that the sides have significantly less resolution to work with.

An illustration of why that is:

The view from a 160, 140, and 120 over a 700x500mm bed: