Signal averaging CCD
CCDs have several types of noise, but only two are relevant here:

Read noise. This is the integration time independent component of the read out process. Every time you read out the circuit you get this noise.

Dark current. These are randomly generated thermal electrons that contribute additional (non-photon) shot noise. As such they are proportional to integration time.


From these it should be obvious that multiple read outs are going to have more read noise and thus will not be better. Less obviously they may not be worse if your dark shot noise component swamps the read noise, but this is uncommon unless your integration time is very long.
For example, a contemporary midrange sensor (which will probably be CMOS since almost no one makes CCDs anymore), read noise might be 4 electrons and dark current 10 electrons per second. The dark shot noise for 2 seconds would be sqrt(20) electrons. Thus if you read out a few shorter exposures you would quickly swamp the dark noise with read noise.
Note that averaging multiple read outs does increase dynamic range, so if you have a very bright signal this may still be a good idea.