A&Vparamo

Assuming he is from any latin american country, not an issue getting a passport. They all issue passports to their own citizen. ID problem solved

If a birth certificate counts as a valid id AND he has it in his possession or can have it mailed to him.. Get the license(literally takes less than 5 minutes- so you are in and out) have your own ceremony and aos.  You’ll probably still want to consult a “ competent” lawyer to wade through any issues that may come up. I quote lawyer part because it seems like alot of persons have issues with immigration lawyers sadly and just end up wishing they did everything themselves. 🤷🏽‍♀️

My number one recommendation it to seek a good immigration lawyer to guide you and tell you what your options are , but for my understanding you might be able to get married without a problem but when you do the process they will require a waiver for his ilegal stay in this country , if the waiver gets a approved he would have to go back to his home country and have a interview with the embassy of the  United States there and if the council decides that  everything is good then he will get his visa to enter the United States legal and his green card . As I said though I’m not 100 percent sure of this the best thing will be to make an appointment with well known immigration lawyer . Good luck with everything !! 🙏

He might be able to get a current passport from his country . He will have to check with the embassy or council of his home country in whichever state he is residing . 

They won't arrest him at the courthouse. ICE isn't there, except by coincidence. You don't even need to be lawfully present in the country to get married here. You just need identification and maybe some proof you live in that state. 
However if he entered without inspection, you're in for a long tough road with likely not a good outcome, I'm afraid. If he just overstayed his visa, then you can adjust status fairly easily (assuming you're a US citizen)

Undocumented does not mean someone does not have documents, usually just a PC term for Illegals.
 
Illegals can marry not an issue and no ICE are not usually the part of any Bridal party.
 
I 601A, pops back for the interview and should be back in the US in a week or so.

if he entered the US legally and overstayed there is a chance under the 245-i clause under the law. I also entered the US in 2000 and later adjusted under that specific law. PM if you need asistance on a referral. The attorney i used is pretty competent on that issue

https://www.nolo.com/legal-encyclopedia/who-is-undocumented-immigrant.html
 
Do all undocumented immigrants sneak across the U.S. border?
Some, but not all. Although accurate numbers are hard to come by, it’s clear that a significant number of undocumented immigrants originally came to the U.S. legally, whether as tourists or on some other nonimmigrant (temporary) visa, and then failed to leave.