Yes, it is normal for the check engine light to come on briefly when the key is turned but not stay on until the engine starts. This is because the check engine light is part of the vehicle's self-diagnostic system, and it is designed to illuminate when there is a potential problem with the engine. When the key is turned, the check engine light will come on to indicate that the system is checking for any faults. If no faults are found, the light will turn off after a few seconds. However, if a fault is detected, the light will remain on until the problem is resolved.
It is important to note that the check engine light does not necessarily indicate a major problem with the engine. In some cases, it may be caused by a minor issue, such as a loose gas cap or a faulty sensor. However, it is always a good idea to have the vehicle inspected by a qualified mechanic if the check engine light comes on, just to be sure that there are no serious problems.