No. Mexico, Isla Roatan, and Belize will subject you from being denied entry.
Legal disclaimer: The statement above is provided by CC Abbott is based on general assistance and not intended to be a legal opinion because not all the facts are provided. The person requesting information and all others reading the answer should retain an attorney who is permitted by the state bar within the jurisdiction who can examine the complete facts and provide a legal opinion on your case. All information provided in the above answer and other information provided by CC Abbott does not create an attorney/client relationship within any state of Federal law.
Since the cruise is going internationally, it sounds like you probably need the advance parole document. If an adjustment of status (I-485) application is pending and you travel internationally without advance parole, you can unintentionally cancel the adjustment application.
If you are trying to depart soon and don't have a decision on the I-131, you can talk to your attorney (if you have one) about trying to get the I-131 decision expedited. In my jurisdiction, it can be difficult to get an expedited decision for pleasure travel, but your area may be different.
If you do not have an attorney, I certainly would recommend you try to find one and at least have a consultation with him/her prior to making any decision about international travel. You can find an immigration attorney through Avvo, the American Immigration Lawyer's Association (www.aila.org) or if you meet the limited income and other eligibility requirements, through http://www.justice.gov/eoir/probono/states.htm.
Ms. Doerrie's answer to your question is general in nature, as not all facts and circumstances relating to the specific person(s) and situations involved are known to her. Ms. Doerrie recommends consulting with an immigration attorney regarding your specific facts and circumstances prior to making any legal decision or submitting any form or application. This response does not create an attorney/client relationship.
You will abandon your adjustment application if you leave the U.S. before your were issued advance parole. You may be able to get an emergency parole through your local district office. It is not a real emergency but they might grant it to you if they are really nice. I recently got an emergency parole for one of my clients who wanted to attend a wedding. You will have to pay the filing fee for the I-131 again. It might be worth a try.
Generally, one may not travel outside the U.S. and then re-enter while still awaiting a travel document. An exception: if the applicant already has the type of nonimmigrant visa, such as an H1(B) visa, that recognizes so-called "dual intent" (both an intention to leave the country when one's visa expires and also an intention to remain permanently in the U.S. if approved to do so).
[Note: Consistent with Avvo policy, this communication is intended as general information and not specific legal advice, and this communication does not create an attorney-client relationship.]
David N. Soloway
Frazier, Soloway & Poorak, P.C.
1800 Century Place, Suite 100
Atlanta, Georgia 30345 www.fspklaw.com
404-320-7000 * 1-877-232-5352 * firstname.lastname@example.org
[Note: Consistent with Avvo policy, this communication is intended as general information and not specific legal advice, and this communication does not create an attorney-client relationship.] David N. Soloway Frazier, Soloway & Poorak, P.C. 1800 Century Place, Suite 100 Atlanta, Georgia 30345 www.fspklaw.com 404-320-7000 * 1-877-232-5352 * email@example.com