Theoretically speaking you can, but you would be better off consulting with an immigration attorney in person when you are here.
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.
Are you a US Citizen? If so, you can travel as much as you wish.
As for him, once he marries you and leaves the US, although the I-130 can be processed ... he'll need to 'stay put' in Egypt for Immigrant Visa processing .... a 7-9 month process.
AND, once his visa is ready, you will need to demonstrate to the US Consul that you have returned, or will be returning shortly, to the US to reside.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
Your question leads to a question. If you are a grad student studying in Egypt, are you earning any money? For your fiance to qualify for an immigrant visa you have to qualify as his sponsor - which means you will have to demonstrate that you have been filing tax returns for the last three years AND that your income currently meets 125% of the HHS poverty guideline minimum. If you cannot show this, you will have to make up the difference in assets or find a joint sponsor. If you would like to discuss this further you can submit a written inquiry to me via my website below. Good Luck!
This response does not create an attorney client relationship and is for informational purposes only. Before acting on this information you should discuss your problem with an immigration attorney.