If your talking the low grade it doesn't matter as the boards usually are ground up or crushed to reclaim the $ out of them. It doesn't matter to my local yard how many pieces the boards are in as their paying me by the lb.
The only time I would desolder is if you have a part that you want to reclaim to resell then desoldering would be the proper way.
P & M Recycling - Specializing in E-Waste Recycling. 
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