The quick answer is yes it can. But the longer answer needs to address whether there is any point in doing that, and whether you would want to.
There are basically two classes of effects, that in recent years have come to be known as 'insert effects' or 'bus effects', both of which are good descriptions.
An insert effect is one where you put signal in, process it, then use 100% of the processed signal and 0% of the original signal. EQ is an insert effect.
A bus effect is one where you want to mix the original signal with the processed signal in the desired proportions to achieve the blend you want. Reverb is a bus effect. You would hardly ever want to use only the reverb sound; almost always you would want to blend in just some reverb with your original signal.
Another interesting point arises from this. Insert effects are best applied to individual signals. However, bus effects can be shared among several signals. So one EQ section only processes one signal. But one reverb unit, or plug-in, can add reverb to several signals.
Compression is almost always used as an insert effect. So if you work in the hardware domain, one channel of compression can process one signal. If you want to process two signals simultaneously, then you need two channels of compression. If you work in software, you need to insert a compression plug-in into every channel you need to process.
That's the Level 3 stuff. How about if you understand all of that fully and want to advance further...?
OK, I have to say that if you are not fully comfortable with the above, then this is going to confuse you, so don't read it.
Compression works by lowering peak levels, then bringing the signal as a whole back up to normal level. So you can often very clearly hear what it is doing to the peaks. Mangling them probably.
But if you connect a compressor as a bus effect so you can blend in the compressed signal with the original, then you can find a blend where the peaks of the original are louder than those of the compressed signal, so you hear the original signal in the loud parts.
But where the signal becomes quiet, the compressed version is louder than the original. So you hear the quiet (but now boosted) sections of the compressed signal.
The end result is a reduction of the difference between the louds and the quiets. And the amazing thing is that when you are hearing mainly the compressed signal, the signal is below the threshold of the compressor, so the compressor isn't actually doing anything!
Master the use of the compressor as an insert effect fully. Then explore what it can do as a bus effect.
Suggestion for comment: If you connect a compressor as a bus effect, should you adjust the amount of compression with the send level or return level control?Come on the FREE COURSE TOUR