Even though the water isn't technically Di water once the inhibitors are added, it is still an "Ultra Pure" water. Almost as with Di water, ultra pure (or really really pure...LOL) water still beads and/or flows more smoothly over a metal (or plastic) surface than distilled water.
It's basically impossible to keep Di water PURE Di water once introduced to a metallic system as bwalker has pointed out...however, with inhibitors, the fluid is still an ultra pure fluid.
As for distilled water and any adverse effects, you'll notice that it is capable of leaving mineral and salt residues behind that can hinder the effectiveness of the cooling system. I cannot speculate as to exactly what negative effect one may have with distilled water...Only that folks have been using distilled for years, we've all seen deposits in our cooling systems and that cleaner is always better in regards to a cooling system.
If what you may be asking is, are there any thermodynamic tests of Di (only...no inhibitors) vs. distilled (only)...not that I have even seen or found. Again, as bwalker pointed out, once Di water hits a cooling system, it isn't Di anymore. So technically, you can't put Di water alone into a cooling system to evaluate it.