Be aware that they do fine people for camping in non designated sites. They would rather you double up on a site, but if there is more than 9 people at the site they will fine you. No place in the rules does it say if you are camping at a site, nobody else can camp there. It only says you must camp at a designated site and more than 9 people cannot be there.
It would be best to ask people first to get how they will feel about it, but IMO, anybody who expects solitude should be going elsewhere, or go DEEP into BWCA to find it. I wouldn't want to camp a a site where I wasn't wanted, but you might be surprised, many people would welcome someone, for a night anyway.
If you object to camping where there is already somebody there, well keep in mind beggers can't be choosy, it is your mistake so live with it.