I don't recall ion cannons doing any damage in X-Wing et al to be honest.
As I recall, ion cannon could blow up TIE Fighters, TIE Interceptors and TIE Bombers (2 hits for a TIE Fighter, more for the others, like the normal lasers) and there was the chance, to disable some of their systems, if you were careful (e.g. flight control, resulting in having them fly straight till they hit the border of the map).
If you blew them up with ion cannons, the message on the lower part of the screen said, "TIE Fighter *** has been disabled", but it counted as destroyed. I'm not sure with mines and TIE Advanced (normally you didn't face these with an Y-Wing within the campaigns) though, but all other ships didn't take damage to the hull. Only to the systems.
And to not leave a detail unmentioned, if your own ship got disabled by ion cannons, it repaired itself (or it was the R2 unit) like it was damaged by ordinary lasers with the exception, that no damage was done to the (graphics of the) cockpit.
Any questions, yet?
Edited by Fregge, 24 June 2014 - 01:10 PM.