It very much depends on whether the police got enough information about the car, tag and driver to make a positive identification later. If there is enough information to issue a warrant in the other county, the person could be arrested.
The person could talk to an attorney and ask the attorney to check if there are any outstanding warrants for his or her arrest. This would be confidential, and at least the person would know.
It's difficult to say whether the police will follow-up with the other county. Eluding requires a failure to stop when the officer displays flashing lights (red or red and blue) and an audible siren. Depending on whether the speeds reached exceeded the speed limit by 25 mph or more, the charge can be an aggravated misdemeanor, which makes one eligible for a prison sentence of up to two years. If you are charged, then you should contact an experienced criminal defense attorney in Des Moines. I suggest Bobby Rehkemper and Matt Lindholm.