xyz_pilot,
If you do report the DUI conviction within the sixty day period, nothing much really happens.
It just goes into your record.
However, after the third report/conviction within a specified period (have no idea what this might be), your license can be suspended for an indefinate period.
A few years ago, was in FCO and one of our crew said he had to report to the FAA international field office (at that time located across the street in the US consular building) and surrender his license for a two week period, because he had not sent proper notification to the FAA security division concerned.
He was further told that a third report would automatically suspend his license for an indefinate period.
He held a separate license so the FAA action did not disrupt the crew pattern.
Apparently the FAA is tracking these reported convictions rather closely, so suspect that those who fail to report will have rather large problems.