Hey there,
Schools run queries on the GMAC database all the time in order to identify talent and build their pipeline. There isn't any distinct advantage to this but if you do share your scores with a particular school, they may reach out to you and try to court you (if your score is high enough).
Also, schools don't trash your scores. It's an online database and they have electronic access. When you apply, you don't need to send scores to each school - you self report and provide, in some cases, unverified score reports (e.g. scanned copy of the print out). If you are accepted and pay the deposit, then you need to send official verification. If, at that point, you're going to a school you'd already sent the score to, then you don't need to resend it.
If you're not applying for another year, and you don't want to have your score out there just yet, don't share it. It's really not a big deal!
Cheers!
Bhavik