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Twitter does in fact implement rel=nofollow to external links on their site but this does not mean content (especially profiles) can not be indexed. Mentioning

• redthrowaway 15y ago
  Individual tweets will be indexed, but google has no idea who's sharing what. That's the issue at hand. Google's changes to Search will promote links that your social connections have shared. If googlebot is ignoring links in tweets, at Twitter's request, then Twitter has taken themselves out of the Search plus Your World game. Again, the issue is not that googlebot doesn't index tweets. The issue is that it doesn't index any of the links in those tweets. Thus Google has no way of displaying "@Someone tweeted this" in their Search plus Your World results.