Set background of entire paragraph text box

Unfortunately, there is no way to extract the size of a text box directly. There is a hack that will allow you to use sliders to scale the text layer and adjust the font size to make it look like you are controlling the size of the text box. Here's the tutorial, it might give you some ideas.

If you want to stick with a text box you have already drawn and you add Effects/Expression Controls/Point Control to the text layer, these expressions on a Shape Layer with a simple Rectangle will work as long as the Shape Layer 1/Contentes/Rectangle 1/Transform Rectangle 1 properties are all at their default values:

//Contents/Rectangle 1/Size
thisComp.layer(index-1).effect("Box Size")("Point")

//Contents/Rectangle 1/Position
ref = thisComp.layer(index - 1);
box = content("Rectangle 1").content("Rectangle Path 1").size;
crnr = ref.sourceRectAtTime();
[crnr.left , crnr.top] + box/2;

//Shape Layer 1/Transform/Position
ref = thisComp.layer(index - 1).position;

 I have not allowed for padding on the background layer.  You could do a little math, or you could just add a stroke to the Rectangle that was the same color tied to an Expression Controls/Slider Control on the text layer. 

That would give you the opportunity to draw a Text Box on any text layer, then adjust the size of the text box background using the Point Control on the text layer. 

I don't have time right now to review the scale of the layer expressions and use that trick to position a background layer behind the text box, but that could also be done. If I get time later today, I'll fiddle with that. Here's my solution with a couple of extra Expression Controls: