I think it depends on the 9, too. Me, I *do* get anxious if things aren't working out right. I absolutely descend to 6. But it's not automatic; it's a slide. Remember, the Enneagram has levels of healthy and unhealthy, and not all will be recognizable. In fact, I daresay that there's a lot of overlap:
Level Descriptions:
Levels of Development Chart
Healthy
1 Level of Liberation: Ego Transcended — Balance & Freedom
2 Level of Psychological Capacity: Ego is Identified with as the basis of a Particular Mode of Being
3 Level of Social Gift: Ego Operating in a Constructive Way, Successfully Sublimating
Average
4 Level of Fixation: Losing Contact with Presence and Awareness, the Beginning of “Sleep” — as Ego-Role assumed
5 Level of Interpersonal Conflict: Ego Controlling Environment to get its needs met — Manipulative & Defended
6 Level of Overcompensation: Ego Inflation, Aggressive defense of Ego-Identity. Demanding that others/reality support the ego-agenda
Unhealthy
7 Level of Violation: Ego willing to violate self and others to maintain itself. Abusive, Devaluing, Desperate (Serious pathology arises)
8 Level of Delusion and Compulsion: Ego-self out of Control and Out of Touch with Reality (Major Personality Disorders)
9 Level of Pathological Destructiveness: Extreme Pathology or death (Psychosis)
Link:
http://www.enneagraminstitute.com/DevelopmentLevels.asp
So a 9 descending to 6 will have qualities of both, but an average or unhealthy 9 will have a LOT of 6-ish qualities (while still retaining 9-ness).