In part Twitter is successful because it allows bots. They make a huge percentage of their userbase. If they cracked down on them, they'd wipe out millions of 'users' and their value would go down.
It also depends on the kind of bots you mean, spam bots should definitely be stopped. But allowing users to post through a bot or an api is great but only for big sites, if you have people automatically posting on a small site it kills user engagement.
> 'is it possible to run a successful social site without that'
It definitely is, the number one reason most social sites fail is that they try to micro-manage their users and the owners think the site will run itself.
Bots and third party tools have a place but only when you have a decent sized site and active community, but they're not necessary.