It will, just got to give the tip a nice tight twist before slipping it into the cup.
I got some 12 AWG Livewire brand from the Guitar Center's bulk wire bin that was pre cut they had priced for $3 for ten feet so I grabbed it knowing very well it was way overkill.
Works good if a bit stiff, made two cables from it. The strain ring also fit over the jacket with room to spare, using the NL4FX connector which is what most complete sets of 12 AWG are sold with.
Neutrik says 12-10 AWG in their specs for the 4 pole,
NL4FX
and 16-12AWG for their two pole.
NL2FX
You must have the two pole?