Screen sound transparency

The screen will reflect sound.

Foam diffusor?...do you mean absorber?
Usually foam is used for absorbtion more than diffusion.
Still, Da-lite should have some more accurate info/stat's for your screen properties/effects, but maybe not!
The short answer is yes, the screen will block sound going to and coming from your absorber/diffusor, and will reflect sound off the front of the screen. Still, sound will pass through from both dirrections, and thus treatment behind would have an effect. Your results will depend on your room/set up and acoustic needs. YOu might tinker with absorb/diffuse and listen for yourself.
Large comercial theaters put massive fiberglass absorption behind their screens, as sound does go through them, yes!
Would I still use absorbtion/diffusion behind a perforated screen?..you bet! Each room set up requires differnt approaches however, and differnt balance of absorb vs. diffuse, etc. You might have to tinker.
You might email Tony Gramari(?) at PMI acoustics. He should sheed some more light on your question.

Thanks, guys! I did mean diffusor (eggcrate-type). I also tend to think, that I should use it in under the screen. Will try to contact PMI. Regards.

There are screens that passes through sound, so your acoustic treatment plan might work out with thenm.