The Manifold Absolute Pressure sensor is basically a barometer, with an electrosensitive diaphram separating the air in your intake from a cavity containing a calibrated pressure of gas or vacuum. It's the diaphram which could be damaged by cleaners.

Fortunately, the sensors cost around 20 bucks (instead of hundreds like the MAF)

no. Verify operation with a diagnostic tool and replace if faulty.

Cleaning a map sensor probably won't help. When maps fail it's not from being dirty rather a break down of the sensor itself. Maps are cheap just get a new one if that's what's wrong

So, what happens if you spray clean MAP sensor?  I did spray clean MAF sensors before but wonder about MAP sensor.

I was also wondering, when replacing MAP sensor, do I need to disconnect the battery cable or do anything extra to reset or calibrate the new sensor?  Or can I just unplug the old one, and plug the new one in without disconnecting the battery cable?  I read different things online and was wondering what the proper procedure is for replacing MAP sensors.

do I need to disconnect the battery cable

I wouldn't. That will reset everything so it'll take even longer for the engine to return to normal operation.

The sensor is low voltage/low current, and the connector is shielded. I can't see any harm that would come from leaving the battery plugged in.