I actually tried it.
To begin with the conclusion, Shadowmere did not respawn.
First, I confirmed that Shadowmere respawns in Vanilla Game. Even if I switched to different horse or Shadowmere died, Shadowmere respawned in "DarkbrotherhoodSanctuaryExterior" after 10 days. Next, as you did, I unchecked "Respawn" of the Base object, saved it as an esp, and enabled this mod. After loading Skyrim, I rode a summoned horse (my own creation) to make "switched state", got off the horse, and let time pass until the cell (DarkbrotherhoodSanctuaryExterior) were reset. Then I went to "DarkbrotherhoodSanctuaryExterior" and rode Shadowmere. After that, I did the same thing I verified in Vanilla Game.
I went to another location away from "DarkbrotherhoodSanctuaryExterior", changed the horse, left this cell, and let 10 days pass. When I returned to the cell where I got off Shadowmere, Shadowmere remained there. Then, 10 days after I killed Shadowmere and moved to another location, Shadowmere's corpse disappeared, but Shadowmere did not respawn even when I went to "DarkbrotherhoodSanctuaryExterior".
This means that unchecking "Respawn" was effective. It does not seem to be related to Alias.
Please check the following two things.
1. The Shadowmere used in the test play is generated as a reference with "Respawn" unchecked.
2. You are not using any other mods that modify Shadowmere or anything related to Shadowmere.