can we achieve signal compression by reducing the sampling rate?
Reducing the sample rate of a signal certainly reduces the data rate, all else held constant.  However, I wouldn't call this "compression".

Without pre-filtering the signal to remove frequencies above 1/2 the sample rate, lowering the sample rate will cause aliasing.

For example, let's say you take a HiFi audio signal of a concert or something where there are significant frequencies above 10 kHz.  This sounds fine when appropriately filtered and sampled at, let's say 44 kHz (the sampling frequency used by CDs).  Now if you decided you only cared about frequencies up to 3 kHz, you don't just lower the sampling rate to 6 kHz.  If you did, all the frequencies above 3 kHz (half the sampling rate) would turn into aliases.  The result would be a mess with all kinds of squeals and weird sounds.  To get just the lower data rate 3 kHz signal, you have to filter the full signal to eliminate content above 3 kHz.  Only then can you sample at 6 kHz and avoid aliasing.

In any case, even if you did the filtering to avoid aliasing, I wouldn't call this "compression".