Seems to be some confusion of definitions here.
Soundproofing usually refers to transmission of sound from the room to the outside, or visa versa. For example, there is a studio in my area that is buried under a large hill. The studio is soundproof, because no passing truck or airplane noise can ever get into the tracking rooms, nor can the music ever bother the neighbors. This has little or nothing to do with the quality of sound inside the room itself - which in a soundproof room could theoretically range from excellent to sucky.
If you create something approaching an anechoic chamber, you are talking about eliminating acoustic reflections in the interior of the room. Almost invariably, rooms like that are terrible to record in, even after adding back ambience with artificially produced reverbs and delays. Adding or subtracting EQ would not alter the fact that natural ambience is missing. It would be kind of like giving a really thirsty person a guitar - a guitar is a useful thing to have, but doesn't have any direct bearing on quenching one's thirst (unless you can trade it for something to drink).