The Thiel Small parameters are mostly influenced by physical characteristics of the sub, so should not be affected much by only using one coil. As well, shorting the terminals of the unused coil WILL have a mechanical impact on the sub, as the electrical energy created by cone movement would be damped, and that would affect T/S and reduce efficiency. Leaving them open would be electrically the same as not having the second set coil present on the sub at all.
I can recall a long time back where some company that made closed-loop servo subs had a demo box that allowed switching between 3 settings, an open sub, shorted coils, and active servo damping, and it was used to show the control exerted on the cone by the damping circuit, and the demo was to simply press on the sub cone and move it by hand. The setting that shorted the coils showed that it would offer more mechanical resistance to movement due to the smaller amount of damping offered by the subs own electrical feedback. A sub moves from the electrical energy put across the coils, and in the same way that a motor and a generator appear to be generally the same, if you manually move a speaker cone electrical eneryg is created and would be measurable across the terminals.
Anyone with a spare sub laying around can try this themselves. Move the cone in and out by hand, then short the terminals and try it again, it will feel that the suspension is stiffer.