There is no difference to the Tweets rendered in an embedded Timeline for logged in or logged out users. Only public content is displayed in embedded contexts (e.g. never protected accounts.) What you see is what every other user sees.
The one place where a user’s logged in state might cause variation is in the Follow button (which is rendered within some embedded Timelines.) Here, if a user is logged in to twitter.com, their authenticated session is used to find out if they are following the account for the Follow button, and if so the follow button is rendered in its subdued, flat state.
As regards tracking: Twitter supports Do Not Track, which is a browser-based technology whereby individual users can indicate their preference to opt-out of personally identifiable logging by service providers on the web. If that sounds like a weak worded description, it’s because it doesn’t have universal support across the web yet, but we do support it. Furthermore, in addition to the browser setting, we allow publishers and developers to apply the same DNT opt-out behaviour to their widgets, on all of your users behalf. If you disable tailored suggestions (e.g. you include the
data-dnt=true attribute in your embed code) then all of the visits on your page are treated as if the user’s browser had sent the Do Not Track header, and these visits will not be used in tailored suggestions for those users, if those users have enabled that feature.
More info about DNT here: https://support.twitter.com/articles/20169453-twitter-supports-do-not-track
More info about how tailored suggestions work here: https://support.twitter.com/articles/20169421
So yes, you can use the timeline widget without tracking any user by adding
data-dnt=“true” to the widget embed code.