Whether a warrant will surface during your in-country flight depends on factors you cannot control. It depends on whether in this age of heightened security someone does check for wants/warrants. Unfortunately, there is no way to tell whether this will occur or not, until you are already in the place where it could occur. Good luck.
Since I do not practice law in your State, this answer is provided solely for informational purposes only, for you to use as a starting point when speaking directly with a lawyer in your State. This answer does not constitute legal advice, create an attorney-client relationship, or constitute attorney advertising. I urge you to immediately contact an experienced criminal defense lawyer admitted to practice law in your State before you make any decisions about this case.
Though an arrest warrant can be sent to other states, this not done unless local authorities take action. So, if someone checks you for warrants in Minnesota, the chances of arrest are high. In another state, that might not be the case, especially before much time goes by.
You may already know that if you have a warrant with a cash amount alternative stated, you can pay the money to get a court date and so avoid arrest and possibly a few to several days in jail.
If you hire counsel, often your attorney may discuss the matter with the prosecutor and reach an agreement to stay the warrant pending a newly scheduled court appearance. If you do not take care of the warrant, you may be stopped for any reason and held in jail on the warrant, even in another state, pending extradition.
I am a Minnesota lawyer and I belive I can assist you. Call 612.240.8005.