I have not done this, but I am somewhat familiar with Anderson products. I don't see where it would be a problem if you make certain that the screws do not hit the glass and are not so long as to go through to the outside. If I remember correctly the doors are about 1 3/4" thick, which gives you plenty of meat.

Because these are expensive doors, and because you're a bit nervous about this application; perhaps you might consider using one of the many custom blind shops that exist all over Florida. It might cost you a bit more, but if they ruin the door, you will have some recourse. Just be certain to tell them your fears and ask them for some assurances. I'm sure they've done this before.