No, it doesn't work that way at all.
Issuing an arrest warrant can not be done by the state Senate. An arrest without a crime would lead to a lawsuit that the police would lose without question.
States do NOT turn people over to neighboring states without proper paperwork and an extradition proceeding.
In order for a person to be extradited interstate, 18 U.S.C. § 3182 requires:
* An executive authority demand of the jurisdiction to which a person that is a fugitive from justice has fled.
* The requesting executive must produce a copy of an indictment found or an affidavit made before a magistrate of any State or Territory, and
* Such document must charge the fugitive demanded with having committed treason, felony, or other crime, and
* Such document must be certified as authentic by the governor or chief magistrate of the state or territory from whence the person so charged has fled.
* The executive receiving the request must then cause the fugitive to be arrested and secured, and notify the requesting executive authority or agent to receive the fugitive.
* An agent of the executive of the State demanding extradition must appear to receive the prisoner, which must occur within thirty days from time of arrest or the prisoner may be released. (Some states allow longer waiting periods of up to 90 days before release).
* Cases of kidnapping by a parent to another state would be automatic involvement by the US Marshals department.
There would be no way to extradite from Illinois since there was no indictment and no judge as issued a warrant. There was no felony to charge them with so that is also not met. Governor Walker could have made up a document and certified it was accurate but that would probably be a Federal crime since there is no crime they could be charged with.
If you know people you can do what ever you want and get away with it to a high degree of abuse!
Only if the abuse doesn't see the inside of a courtroom or the front page of a newspaper. If Walker and the WI Senate had tried to extradite the missing Senators they would have found themselves subject to an FBI investigation.