That is highly doubtful; bench warrants (especially misdemeanor warrants) remain in what is called the criminal information index, which is a state database used by law enforcement. No warrant checks are done when checking into a flight. As a general rule and practical matter, you should clear up the warrant, however, which is a simple matter of going to the courthouse where the warrant was issued. Go to the clerk's office and let a counter clerk know that you're there for a warrant recall. If you FTA'd to do jail time, however, you'll probably be immediately remanded into custody. Good Luck & God Bless.
Many arrest warrants are not even in the system and are simply being held by a particular law enforcement agency until they pick a person up. Whereas a bench warrant is issued by a court and much more likely to be found and acted upon by airport law enforcement. I have many clients who retain me that have been arrested in the airport based on an arrest warrant and / or bench warrant. Since 911 and the advent of Homeland Security the airports are much more vigilent regarding checking identification and a person's status. You are much more likely to be arresting coming back from going out of the country. In some instances I have been able to get a particular judge to recall a warrant in order for my client to be able to come into the country without getting arrested and resolved their matter.