Did you move the anechoic chamber? That process might be an interesting write-up once you're all settled.
Yes it will. The new test space is a fully underground 600'+ concrete basement -- floor & walls are concrete. Ceiling is the underside of the floor above, a portion of which is being insulated now. Without any acoustic treatment & one pretty quiet PC going on the other side of the room, the SPL is 13-14 dBA. Pulling the fans from the acoustic measurement PC might drop it a bit further, but I'm going to put up sound absorbing "blue fill" baffles before doing that.
The new space is about 4-5 dBA quieter than the old room before treatment. Mostly because of the damping underground & because there are no sources of noise around here -- I'm now living on an island 30 miles from Vancouver, in the Georgia Strait between Vanc & Vancouver Island. There are small float planes that fly overhead from time to time, maybe 10x a day, but the sound of each does not last long.
I'm building modular sound absorbing baffles, like thick dividers in open offices. They will be on wheels, moved out of the way when not needed, and stackable. I built the first pair -- roughly 4.5' tall, 4' wide, >1' deep. Sort of like a deep bookcase. Another one goes on top of this, same dimensions but 3' tall. I'll build 6 pairs to start. This will be enough for a circular space of 9~10' diameter with very low reflection. I will position it a good distance from the walls. It should bring the SPL down to 10 dBA or better. If needed, I'll make 2 more pairs of baffles to create an 8' cubic space, or inrease the thickness of the baffles by 50%. There will be a slight gap between the ceiling & the baffles, but from experience, I know this has no effect unless there's noise elsewhere in the room/house.