Is there a better way of avoiding drawing the large texture every frame besides the one I gave? Do these optimizations even matter in XNA?
This is the question I personally would ask before doing this type of optimization. Depending on the hardware targeted, and what calculations are being done CPU side, I could even believe it would be slower.
The best way to know for sure is to profile, even a quick & dirty "stress test" with FRAPS running (if on PC) in the background could tell you if the easier solution (just let the GPU cull pixels) is fast enough.
I often found that iterating over sprites or other data structures CPU side (for large collections) is usually the bottelneck; pushing everything to the GPU (properly batched) is pretty fast, on modern PC hardware. However, culling sprites can be important if you are doing heavy calcs on a large set, e.g. physics or collision detection.