The way I understand what you want to do is to essentially have a transparent window in the middle of the Styrofoam insulation panels.
It seems to me that this would work. Your R value would drop down to about R1 in the clear area of your pop-in foam panel, but the overall all R value would still be good if the clear part is fairly small.
I would consider using something like Atlas R-Board instead of the polystyrene foam board. The R-Board is polyisocyanurate insulation, which has a higher R value, and the R-Board has face sheets that look nice and might provide a bit of fire resistance. The polyiso insulation also has a much higher temperature capability, so it won't melt as the polystyrene might. Here is a picture of one shutter we made with R-Board:
http://www.builditsolar.com/Projects/Co ... ngDoor.htm
A couple alternatives:
We use inside storm windows made from triple wall polycarbonate. This is about R3, and provides lots of daylight and some view (but the view is a bit distorted). The panels are easy to make, easy to install, and should last for many many years. You can leave them up all year or take them down for the summer.
http://www.builditsolar.com/Projects/Co ... Window.htm
The polycarbonate material is very tough -- its the football helmet stuff, and its treated with a UV resistant finish.
You could also use a single sheet of clear Acrylic plastic. This stuff is so clear that you can't see it at all, and it can stay up all year if you don't need to open the window.
There are a couple of these described here:
http://www.builditsolar.com/Projects/Co ... Treatments
They can be held in place with just Velcro, which makes putting them up easy. Around here, it runs about $2 per sqft.
You can estimate your fuel saving for storm windows with this calculator:
http://www.builditsolar.com/References/ ... pgrade.htm
It will estimate the savings for the increase in R value, but will not do the savings due to air infiltration (if any).