relationship between energy and sampling rate
You must observe the nyquist frequency when sampling a signal. 
In order to sample a signal without introducing artifacts, you must first filter out everything in the signal that has a frequency higher than half of your sampling rate.  If you sample a 1000Hz, then you must first filter out everything above 500Hz.

Yes, changing the sampling rate can change the bandwidth of digital representation of the signal.  A lower sampling rate means a smaller bandwidth.

This will only improve crosscorrelation if the noise is all high frequency stuff, and the signal you are trying to detect is in the lower frequencies.  You could get the same effect, however, by using a low pass filter  on the sampled data.  That would also remove the high frequencies and make the correlation clearer.