"Check Engine" Light, And Cars Computer ?

Hello:

Have been getting a "Check Engine" light on my '97 Buick Le Sabre.

Totally random.  Sometimes on starting, other times while driving.
No discernable difference in cars performance whether light is on or off.

If I bring in for service, Murphy being Murphy, am convinced light would
probably be off for them.

Question:  Once light is on, is the fault indication stored in the cars
computer, so even if light is off when
brought in, they can diognose what caused it ?

Thanks,
Bob