It's not 100% clear, but by my reading of Internal Revenue Code section 1411(c)(1)(B), I don't think this would be allowed. Net investment income is reduced by "the deductions allowed by this subtitle which are properly allocable to such gross income or net gain." I would think an itemized deduction is not "allowed by this subtitle" to a person who does not itemize. (Oddly, the Treasury Regulations don't seem to address this. It would be in Reg. 1.1441-4 if anywhere; there are extensive rules on how to apply now-defunct itemized deduction limitations but nothing on people who don't itemize.)
Maybe you can take a position that it's deductible (allocable state taxes are more generally "allowed" even if not specifically to you), but don't be surprised if the IRS disagrees, and prevails. And as noted above, if you override you can't e-file.
