It depends on how you accomplish this. In OTL, you had the establishment clause because the various state establishmented religions wanted assurances that the feds wouldn't interfere with them. Likewise freedom of speech was already a cause celebre. Look at the ratification debates, you'll see that both brooked large.
So if your POD is to get rid of the state religious establishments early, that's a big social and ideological change that's going to have other effects. If its to get rid of the Printer's Case, that will have other consequences too, though maybe not as many. If you have the Federalists renege on their promise to pass a Bill of Rights, well, that means a very early end to the Federalists and a Bill of Rights anyway.