By your question I assume that you mean that you were convicted of operating while intoxicated on 3 separate occasions in Wisconsin. If that is the case, those convictions remain on your record. Maintaining a Wisconsin address and avoiding detection are irrelevant. Those 3 convictions will follow you whether you live in Wisconsin or any other state. If you are arrested again for OWI, your driving record will be examined and your next will be a 4th.
If you apply for an Illinois driver's license you will likely find you are ineligible because of a conviction for OWI in Wisconsin, and will need a formal hearing in Illinois to be considered for a license.
Have the prosecuting agencies issued complaints against you? If so, the statue of limitations has tolled (i.e., is no longer an issue). To comply with the statute of limitations, all the prosecutor has to do is file a complaint. Compliance is not dependent upon you showing up in court. Think about it: If fulfilling the statute of limitations depended on the defendant, everyone could avoid court and have their charges dismissed. It does not work that way.
Also, the time you live outside the State of Wisconsin does not count toward the statute of limitations.
But, you are asking if the OWIs will go on your record. You will not be convicted if you avoid court, but a bench warrant will be issued for your arrest. If you are out of state and arrested after being stopped for, say, speeding, Wisconsin will not extradite you for a misdemeanor. Instead, you will sit in jail in whatever state you are in for days, weeks, maybe even months, waiting for Wisconsin to tell the other state you will not be extradited. You will be released, but that will not take care of the warrant. A year later, you are stopped for, say, jaywalking, and taken in on the warrant again. And, this whole process starts over.
IMO, it is just not worth trying to game play the system. You should hire an attorney and face the charges.
Ms. Missimer not only responded to your actual question, but provided the only proper answer to it. The statute of limitations only applies to the time it takes the prosecuting agency to file the charges ("issue the complaint").
Rather than trying to live like a fugitive, you will likely be better off talking confidentially with an attorney or three who could represent you on all outstanding charges and getting your self situated in a county where house arrest/electronic monitoring is likely (assuming that the counties you are charged in permit jail sentence transfers to counties which allow electronic monitoring - experienced, competent counsel should be able to answer that question for you too).