Not by default. Historically, TeX uses an asynchronous model because changing one part of the document could cause changes elsewhere. On a modern system, unless the document is unusually long or complex, clicking the Rebuild or Typeset button refreshes the typeset window very fast.
Synchronous typesetting requires a different approach, and there are commercial systems like Scientific Word which use TeX in this way. LyX is an open-source near-synchronous system which you might like to look at.
There is also InstantPreview and the TeX daemon, and a number of close-to-synchronous systems implemented as add-one to 'normal' TeX.
By 'live preview' I assume you mean 'in the same window while you type'. This is synchronous editing, like a wordprocessor.