Could he still be deported while the forms are being processed?

Yes, hire an attorney. You still need to file an Affidavit of support and, if he overstayed his visa, a waiver for the overstay. You will also have to provide documentation showing that this is a legitimate marriage and not one for immigration purposes only.

Make sure your husband stays out of trouble: even a smallest brush-up with the law can trigger his arrest and detention by the immigration authorities. I have seen such arrests after a ride on a bus without paying the fare, and after being assaulted in a bar fight. Make sure your husband has with him, at all times, copies of his expired visa, Form I-94,and of the receipt for filing the I-130/I-485. If he does meet with an immigration enforcement official, having these documents will save your husband some time and trouble. For the same reason, it is advisable to have an immigration attorney who is familiar with your husband's case and is ready to intervene if it becomes necessary. Finally, make sure that you answer all letters you might receive from the immigration - and do it before the deadline your response is demanded. Considering that a letter from USCIS might get lost in the mail, make a habit of checking the status of your case on-line at least once in 2 weeks at https://egov.uscis.gov/casestatus/landing.do If you move, remember to notify USCIS of your change of address - both on-line and by mail. Good luck!