It's untowered, so I guess it would be legal. Not sure your insurance would cover you, however. (Not saying it won't!) I've landed on a taxiway before in similar circumstances at KWYS. These are the NOTAMs I see. Note that the AIRPORT isn't closed.
Iowa City IA [IOW]: August NOTAM #1 Runway 25 precision approach path indicator out of service effective from August 03rd, 2009 at 04:00 PM CDT (0908032100) - September 08th, 2009 at 11:00 AM CDT (0909081600)
Iowa City IA [IOW]: July NOTAM #13 Runway 7/25 closed effective from August 03rd, 2009 at 06:00 AM CDT (0908031100)
Iowa City IA [IOW]: June NOTAM #3 Runway 12/30 closed effective from June 08th, 2009 at 07:00 AM CDT (0906081200)
Iowa City IA [IOW]: June NOTAM #10 Runway 7/25 intersection with runway 12/30 personel and equipment working VCNTY effective from June 24th, 2009 at 07:00 AM CDT (0906241200)
Iowa City IA [IOW]: August NOTAM #2 Runway 7 precision approach path indicator out of service effective from August 03rd, 2009 at 04:00 PM CDT (0908032100) - September 08th, 2009 at 11:00 AM CDT (0909081600)