1. Not sure where you got the "state misdemeanor warrants not entered thing." First, untrue and second, there are many more systems than NCIC out there and third, they do work together sort of.
2. A good chance you are arrested. Possible you slip through the cracks. What happens depends on your status.
3. If you are a USN, you will be detained pending notification of the agency which holds the warrant. Depending on the seriousness of the misdemeanor, the relative distances and local policies, they may or may not pursue you. If they do, you will be held by CBP as a courtesy pending the arrival of the agency holding the warrant. This can take anywhere from hours to a couple of days.
4. If you are not a USN, you will likely be excluded and returned to wherever you're from.
There's no great rhyme or reason to the system, but the real downside is that once flagged, you will wind up being pulled out forever more both by CBP and other countries with whom the USA shares information. Worse, people miscode items and your misdemeanor gets miscoded as some huge deal.
All of this said, presuming that this isn't hypothetical, the sole solid piece of advice is to get a real lawyer. The only thing dumber than not clearing up the underlying mess is relying on what you're told on an Internet forum.