Talking about suicide is not at all the same as suicidal ideation.
Talking about suicide implies thoughts about suicide, and the definition of suicidal ideation Vaniver quoted says such thoughts demonstrate suicidal ideation. If so, talking about suicide implies suicidal ideation.
There are narrower definitions of suicidal ideation (e.g. the two you cited earlier) but I worry that broad definitions like Wikipedia's prime people to interpret discussion about suicide in general as a reliable sign of suicidal ideation or being mentally unbalanced. jooyous might have a similar concern.
(I'm not saying you're doing that in this case. Someone mentally simulating suicide on an ongoing basis clearly is engaging in suicidal ideation.)
I sometimes have thoughts of suicide. That does not mean I would ever come within a mile of committing the act of suicide. But my brain does simulate it; though I do try to always reduce such thoughts.
But what I have noticed is that 'suicide' is triggered in my mind whenever I think of some embarrassing event, real or imagined. Or an event in which I'm obviously a low-status actor. This leads me to think that suicide might be a high-status move, in the sense that its goal is to recover status after some event which caused a big drop in status. Consider the following instances when suicide is often considered: