It is legally permissible for a J-1 noncitizen to travel outside the United States while the waiver process is in its early stages. Once the favorable recommendation has been made by the Department of State, it is very inadvisable for the J-1 noncitizen to travel outside the United States.
Having said that, one needs to keep in mind that it is not unreasonable for a Consular Officer to ask about the waiver process or intentions and use that as a negative factor to refuse visa issuance.
Consequently, the best advice is for a J-1 noncitizen to abstain from international travel after the waiver process has commenced.