Not without risk.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
Just to be on the safe side, I would wait until a receipt notice is received from USCIS. Having a marriage certificate doesn't necessarily prove that you have an application pending.
Generally speaking, traveling within the US shouldn't be a problem. However, if you need to use your foreign passport as proof of ID because you don't have a valid driver's license, then that could trigger a DHS officer to inquire about your immigration status. If you are a visa overstay, for example, that would mean that you are in the country unlawfully. Having the receipt notice would be more acceptable proof (in my opinion) that you are doing what you must to resolve that issue. Good luck.
[This answer is for general purposes only; it does not constitute advice and does not establish an attorney-client relationship.]
Neither the I-130 or I-485 are travel documents. Your I-131 is your travel document, which will take 60-90 days to be approved as long as it was properly filed. The travel document is meant for international travel, not domestic travel.
You do not need special documentation to travel domestically in the US.
However if you are not in a legal status not (and no pending Adjustment of Status is not a Legal Status), you may be detained or questions by immigration authorities and even placed into removal.
You should consult with an attorney to reverse engineer what you have done so that they can help you understand the what your status is and what you can do while on it, i.e. travel, work, etc.
Representing clients throughout the US and around the world: www.PogueImmigrationLaw.com (513) 549-4420. We cannot provide legal advice or recommendations unless you retain our law firm to represent you. No attorney/client relationship will begin until you sign a representation agreement and make a retainer payment to open a case with us. Any information found here is general in nature and should not be relied upon in individual cases.
And foreign passport
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: firstname.lastname@example.org; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.