The PCM has "Learning" capability that allows it to make corrections for minor variations to improve driveability.
If the car battery or PCM is disconected, the "learning" process resets and begins all over again.
The PCM can relearn operating parameters in a short driving period.
However, if the PCM memory is lost and the car is not driven ( to relearn) prior to returning to the customer, the customer may notice a change in car Performance for a short driving distance.
Note: Anytime the PCM losses power, the I/M Readiness Flags (software) will be rest to OFF.
To reset the flags, drive the car through a FULL OBD-II drive cycle

Crank (CKP) Sensor Relearn Process
Requires a PCM scanner to command the PCM to enable CKP system variation learn fuel cutoff and allow the crankshaft position system variation compensating values to be stored in the PCM.
The PCM must detect an engine speed of 5,150 RPM during the Crankshaft Positon System variation learn procedure in order to store the crankshaft position system variation compensating values and complete the procedure.

NOTE: By not doing a valid CKP test, engine misfires can occur until crank positon is known by the PCM.

The Crank Position relearn process is pretty interesting. Does the power interuption also cause this relearn, or is it only induced by the scanning tool? It would seem an odd situation if a dead battery sets the relearn process and the driver never gets the rpm's to the required level to complete the process.

What is important to know is the crank position is used to determine if there are misfires and which pistons are involved.
If the crank position is not properly learned, false misfires might occurr.

Your right, any loss of power would require any important sensor to be learned, not only for issues like crank, but many of them are part of the math forumlas PCM uses to decide how to tune up fuel trim tables, amount of timing etc.

Also correct if after a loss of power to PCM, if the owner does not know this and not get to that RPM, the test is not completed or can flag false errors.

That's why it is important to know what these electronic controlled engine require.

The scanner, if it has the feature allows the service guy to assure this CKS is learned correctly but can be done via the drive cycle procedure.