No. The inmate is not held responsible for a visitor's outstanding warrant. The background check process catches these things and the visitor will simply be denied approval, but the inmate who submitted the request is notified and not punished. They are not expected to know whether someone they care about has a warrant in another jurisdiction.
The person with the warrant, however, should take this seriously. If a warrant is discovered during the facility's background check process, the information does not automatically trigger an arrest at the prison gate. But having an active warrant is a risk that follows a person everywhere. In Iowa or any other state, an active warrant means law enforcement can detain that person at any point during any interaction with the system, including at a correctional facility. Showing up to visit someone in jail or prison when there is a warrant out is taking a real risk.
The right move for the person with the warrant is to address it before it becomes a bigger problem. An attorney can help navigate voluntary surrender or other resolution options that typically produce better outcomes than being picked up unexpectedly.