Is it OK to add extra paragraph to a paper during the proof stage?
In general no. There may be some circumstance when it can be necessary but the proofing stage is too late for any substantial changes. The manuscript should be published in the form it has been accepted and it is an authors responsibility to provide a final version of the manuscript which ideally should not require any changes once type-set and provided in the form of a proof. Changes that are acceptable are changes that do not in any way change the science of the paper. 

If  any major changes are done to the paper at proofing, the editor will likely decide whether or not these are permissible. What would happen if anyone tries to push substantial changes altering the core science of the paper probably varies, but in the worst case the paper might have to undergo new review.