Okay to use virgin spare?

[ree]

Despite my best efforts to rotate/align/balance frequently, one of my BFGs is going downhill fast. It's really unevenly worn, makes a ton of noise, and shakes at various speeds. I wasn't planning on upgrading to 37"s for another few months but this one tire is driving me nuts.

Is it okay to use my spare that's never been used for a few months until I get new shows? I was stupid to not rotate it along with the others. But that's the way it is. It's treads are about 6-7 mm deeper than the other tires. Or will doing this wear on the diffs too much?