It will untimely be up to the judge to decide. All the person can do is explain to the judge about the homelessness and the lack of money for not completing the class. Some DUI classes have sliding scales so look into that. When I went to court, I would get a letter from the program that you have contacted them and are awaiting a referral from the court to enter the class.
Mr. Tiemann is absolutely correct when he says it's really up to the judge. The person you mention should explain his situation to the judge, and if the judge is in a good mood or very understanding then everything should be okay.
Document your income and living arrangement history, add the case onto the court calendar, seek to have the warrant recalled and explain why you have not been able to adhere to your probation conditions in the past, and why you NOW will be able to do so, thus are entitled to another reinstatement to probation. If you now have the resources to hire an attorney, he/she may be able to handle all this for you without you personally having to go before a judge.
There are many factors to consider. Having the past due money with you also helps. Going into court, late, with no money and a million unverified excuses will virtually gaurantee being taken into custody.
Will the judge really listen to the excuses provided by the defendant. Many judges have busy calendars and will sometimes make an early morning example to other defendants by taking into custody anyone with a probation violation. If the judge will actually listen, then the defendant must have proof of homelessness. Saying you were homeless versus showing tangible proof of homelessness will bring different results.
Having an attorney appear for you or with you helps. Many judges don't like the hassle of dealing with 'Pro Per' defendants because they may not understand the court lingo or may not know how to respectfully and intelligently negotiate with a busy judge. An attorney will (or should) know the judges temperment and their dislikes.