What areas are you treating in the rest of the room? The reason I ask is that your question makes me think you may be over-treating your room.
To answer your question: It is most likely not necessary to treat under your screen. Will your center channel be under the screen? If it is, treating could actually hurt your sound quality (depending on how the speaker is ported). I wouldn't treat under there unless you have a specific reason why you think it would be necessary.
> Is it necessary to treat the wall underneath the screen? <
The two most important places to treat are 1) all the corners for bass trapping, and 2) the first reflection points on the side walls and ceiling. After that, if more absorption is needed to tame any remaining ambience or obvious flutter echoes, more absorption can be placed in appropriate locations.
My question arose because I’ve always understood that it’s important to completely deaden the front wall.
As far as my general plan. I’m starting with very little treatment in the room. The front corners will get floor to ceiling corner fill base traps. The rear corners will only be treated 2’ from the ceiling to begin with (mainly for flutter echo). The mains will get 2’ x 6’ x2” deep absorption panels directly behind them. The 1st reflection points on the sidewalls will be treated with 2’x4’x 1” absorption panels and the ceiling with a 3’x6’x1” suspended ceiling panel. The rear wall is used for CD & DVD storage so this creates a great diffuser on the back wall.
At least that’s my plan.
By the way, the room dimensions 12’ x 17’ x 7.5’ (completely sealed room).
Are you main speakers ported? If so, where is the port? If the port faces the back, dampening a lot behind it could really change the sound of the speaker. I'm not saying it will necessarily make it worse, but I wouldn't do anything permanent without testing it first.
>I’ve always understood that it’s important to completely deaden the front wall. <
I know this is commonly recommended, but it's not really necessary. Maybe if you have dipole speakers that play through the front and rear. Otherwise, the front wall needs no special consideration in my opinion.
> The front corners will get floor to ceiling corner fill base traps. <
Yes, bass trapping is extremely important. Much more than most people realize. All of your other plans are right on the money. It looks like you've done your homework!