Well the judge can impose additional time for the probation violation as well. The typical sentence to pay off all the fees and fines in 13 days but the judge can require more time in jail.
If he would have converted the fine to jail time initially, most, but not all, of the fines could have been served by two weeks in jail. Any amount he already paid will be deducted from the total amount due and he can convert the balance to jail.
If they're alleging a violation of probation based on a failure to pay fines, they must prove he was in "willful" violation. If he truly could not afford to pay the fines, it's not a "willful" violation. Judges tend to frown on that excuse though. Can they add on more time than the straight conversion? Maybe. It depends on his record, whether or not he's done the other things he's supposed to have done (signed up for the DUI classes, etc) and how long it's been since he stopped paying. If this is a first time DUI, technically, he's got 6 months hanging over his head.
It's always better to request an extension than to have it go to warrant and then try to explain it away.
Most DUI fines can be paid by serving two weeks in jail. Your boyfriend would get credit for any amount he has already paid. The fact that it has gone to warrant for failure to pay creates a problem as initially, prior to be granted probation there was the potential of going to jail for 6 months. Assuming he has done everything else, DUI classes, AA meetings (if required) the judge may add more days than the original two weeks because it has gone to warrant. Your boyfriend should have gone to court before it went into to warrant status and requested this modification. Having an attorney would probably help reduce his jail time.