Sensitivity is just the slope of a plot of signal (y) versus amount (x). Often, when speaking informally, one will use sensitivity as a measure of detection limit, but this is not the recommended use for the word. So...
Preconcentration is a means of lowering the overall detection limit of your method; think of it as the inverse of dilution. It does not make your detector response bigger for a given mass of analyte injected into the column. It does increase the detector response for a given amount of specimen.
You can change the detector response by changing the chromatography. Making the peak elute earlier by changing gradient, buffer, column length, etc. will make it narrower and higher, so if you are using peak height, your sensitivity increases. Anything that compresses the same mass of analyte into a smaller volume of mobile phase will increase the sensitivity of detection.