Putting an HPF in the sidechain reduces how sensitive the compressor is to frequencies below the knee of the HPF. Essentially less compression triggered by the lows.
Well... I know what you're trying to say, and effectively yes, but... an HPF in the sidechain reduces the level of low frequency content in the detector signal which may trigger the compressor. A single band compressor is not any more "sensitive to lows" than it is sensitive to the entire incoming signal, regardless of what's going on in the side chain. The compressor threshold is a loudness parameter (decibels) independent of frequency (Hz). Any peak in the audio signal will trigger the the compressor based on how much the peak exceeds the threshold, by an amount set by the compressor ratio, regardless of what specific frequency the peak occurs at.
Splitting hairs at this point, I know.
For example. If you had a compressor with a sidechain input, you could feed the comp a send from the kick drum, high hat, or a metronome click, or some drunk idiot screaming into a mic whenever he pleases... whatever. The compressor threshold only "sees" the sidechain signal, but acts on the audio signal, So whatever is happening in the sidechain... that click could be 40 Hz or 10,000 Hz or anything in between.... doesn't matter. When the detector/sidechain signal exceeds the threshold, the compressor will trigger and clamp down on the audio signal.
HPF sidechain only reduces the level of the low frequency content in the detector signal, with the intent of making the true attack peak of the note more "visible"... Instead of a gigantic signal bump at 100 Hz overwhelming the detector threshold, now the comp can "see" the true peak of the note attack more precisely, allowing you more precisely dial in exactly what you want the compressor to do when the note hits.
The way @Wasnex has described is closer to multi-band compression, where you have completely separate and independent threshold and ratio parameters for different frequency ranges. In that case the lows and highs are actually compressed completely independently from one another. You're effectively splitting the signal with a crossover and sending it to two separate compressors, then recombining the compressed signals at the output.