First off, the permission such as Advance Parole or Visa is required to ENTER into the United States, and not to LEAVE the United States as you mentioned.
Secondly, once an alien has a pending I-485 (Application for Adjustment of Status), s/he is required to have advance permission to allow him/her back to the United States since s/he doesn't hold any STATUS. Just because an alien is married to a US citizen and/or has filed an application I-485 then that doesn't mean that such alien already has STATUS. Further, immigration laws state very clearly that if an alien leaves the country without obtaining advance permission from USCIS when s/he has a pending application I-485 then such pending application would automatically consider to be abandoned. That's why aliens who have pending I-485 application are required to have advance parole if they want to return back and if they don't want their application to be abandoned.
However, once an alien has already secured/adjusted a status then s/he doesn’t need any permission from USCIS unless s/he wants to leave the United States for more than 12 months. Permanent Residency is a status being an immigrant visa. And a permanent resident is allowed to leave or enter the United States as many times s/he would wish even if s/he might have a pending citizenship application. But a permanent resident is not allowed to stay more than 12 months in one single trip outside the US unless advance permission (Re-entry Permit) is obtained; otherwise his/her permanent Residency status would automatically be revoked. And no need me to say that s/he then also breaks the continuous residency requirement for a citizenship as well.
Bottom line, you don’t need any permission even though you have pending citizenship application. Only thing you need to make sure is that you don’t miss any appointment like fingerprinting or interview, or their REF if USCIS would demand some documentation while your application is processing. Usually, USCIS don’t demand any documentation while application is processing, because they ask any kind of document only during the time of interview. But I’ve seen some people were asked some documentation while their application was processing. So, you cannot rule out anything when you deal with USCIS. Just make sure that you won’t miss any mail from USCIS.
