There are better and safer options. Welding the spider gears is something that's commonly done on domestic drag cars and such, but doing so totally locks the differential and puts added stress on the differential and driveshafts while turning.
It's even funkier in the snow. The back end will start to track all over when you get on the slipperies. Having them locked together means that one is always sliding when doing anything other than strait line driving.
I would not recommend this for anything other than a junker car that you want to do donuts in.
i dont have lsd, and I always spin both off the line. I did a huge burnout one time and did a couple donuts, had them both spinning the entire time. I wouldnt worry about getting lsd unless you are drifting or have serious power you need to lay down.