Codes Stored with no CEL?

[Dan DiBiase]

My A4 is having a very intermittent stumbling/hesitation issue. My wife has had the problem numerous times, in heavy traffic, while I
haven't really been able to replicate it. I just had the timing belt (etc) changed, so I am wondering if it is related. Or perhaps a clutch
slip. Will the on-board computer store any codes that may be generated even though there is no, nor has there been, any Check Engine
Light flashing or warnings?

 Dan D
'04 A4 1.8Tq MT-6
Central NJ USA