Could Spartan IIIs have relationships with others?

I know for the Spartan IIs there was a risk of a reduced sex drive. However it was only a risk and only one Spartan II we know has it. Did Spartan IIIs have the same risk as the IIIs. Also were there any Spartan IIIs have relationships with others. The only source I know is Martin O'Donnell saying, "We know there was some relationship between Carter and Kat at some point." Which I don't know if it is canon or a joke. Is there any information on this?