My interpretation is that most Rider dragons would suffer much from it, because that is built into the Rider bond, to ensure they would always have a supply of Eldunarí and to make it possible to control dragons who wanted to escape. The wild dragons would never have had this problem.
For Restitution, I am certain the dragons of the Forsworn broke their own Eldunarya, in order to escape from the Riders. Seeing as they were soon affected by the Banishing of Names, the pain from the loss of their Eldunarya was very light in comparison.
I think it might be comparatively easy for Thorn to lose his Eldunarí in that way, since he has already suffered much during his time under Galbatorix.

And I am quite certain the destruction of the Eldunarí would make using magic more difficult, though not impossible, as it functions as a focus for magical energy.