Is it possible to run functional tests without creating test tables?
I have found the answer there. But don't do that ! 

It's better to move the database on a tmpfs folder (it's > 5x faster), because not only a "dirty" environment does not work, but it will broke your website with a serious error (just happened to me).
Hints to tweak the database on this question.

It's there but don't do it :

  // for our functional testing, we want to test the pages and code that
  // we've been generating in the real database. to do this, we need to
  // ignore SimpleTest's normal fake database creation and fake data
  // deletion by overriding it with our own setUp and tearDown. NOTE that
  // if we make our own fake data, we're responsible for cleaning it up!
  function setUp() {
    // support existing database prefixes. if we didn't,
    // the prefix would be set as '', causing failures.
    $this-&gt;setup = TRUE; // Drupal 7 way
  }
  function tearDown() { }