Is your fiance being detained due to an "ICE hold"? If so, it is unlikely that he will be released on bond anytime soon.
Immigration and Customs Enforcement (ICE) is the governmental department that deals with deportation. When someone who is undocumented commits a crime, and ICE is notified that the person does not have proper documentation to be in the US, they will put a "hold" on the person's release. If this happens, the person is not entitled to bond under the Arizona constitution. This means that they stay in custody until their criminal case is resolved...and, once that happens, ICE has the ability to keep them in custody and determine if they should be deported.
As for whether your fiance will be deported (or, "removed" as ICE calls it), you should consult with an attorney who is familiar with these issues since the laws are constantly changing. The laws about deportation for conviction of a DUI are confusing. A DUI on a suspended license is a felony, and the Ninth Circuit Court of Appeals has held that this a felony DUI for driving on a suspended license is a "crime involving moral turpitude" under the Immigration and Naturalization Act. If you would like to read the entire opinion of the Ninth Circuit, it is available here: http://www.ca9.uscourts.gov/datastore/opinions/2009/03/04/0476644.pdf
Under the Immigration and Naturalization Act, even someone who is here on a valid visa can be deported for a crime involving moral turpitude for which they are imprisoned for at least 1 year. An aggravated (felony) DUI is punishable by up to 3.75 years in Arizona. Although these cases are typically resolved by plea agreements for 4 months, they could still have immigration consequences.
Long story short, before your fiance considers a plea agreement, it is imperative that you meet with an attorney who is familiar with the immigration laws to ensure that the plea agreement does not affect his ability to remain in (or return to) this country. Your fiance's public defender may have a level of comfort with the immigration system, but if he or she does not, you should contact a private attorney asap.
Best of luck,
If he has a domestic violence conviction, he will be deported and not allowed to return legally. Otherwise, if he doesn't, then he can sign a voluntary departure possibly. He wouldn't be able to apply for a Visa for ten years.
You should consult with a good reputable immigration lawyer.
This isn't legal advice, it's only a public discussion.