@Winston Go to settings > profile > uncheck "List profile in the directory"
As for your question: unless you want to be surrounded by illegal paraphernalia sellers, child porn, and gore photos, then it's a bad idea. And that's IF you can find a social network on the deep web!
But hey, nothing stopping you from starting your own Mastodon instance there and inviting all your friends, if you so choose. 👍 Though you'll need to prepare your to keep out all the cocaine salesmen, I imagine!