Only during the investigation and any subsequent criminal proceeding in Sweden. After these are completed, or abandoned, he could be extradited from Sweden to the US. From the blog post linked in section two of the New Statesman article:

"After the investigation and any criminal proceedings in Sweden end, that restriction also ends and the Swedes can extradite him without reference to the UK government. But neither Sweden and the UK will extradite anyone to a country where the accused is in peril of the death sentence if convicted of an offence, or where prison conditions are so bad as to breach his rights under Article 3 of the ECHR (‘No one shall be subjected to torture or to inhuman or degrading treatment or punishment’)." [1]

[1] http://ffgqc.wordpress.com/2012/06/20/julian-the-asylum-seek...