I have tried to utilize a compressor to extend sustain of notes while playing lead guitar. I have used it in conjunction with various distortion and boost pedals and delays. I am trying to achieve a sound similar to my late 60's Marshall plexi played at max volume but at a more tolerable volume level. With the plexi you get a singing sustain almost like the human voice or possible a violin with a sag that I can't seem to duplicate a lower volumes on any other amp. Is a compressor set to the proper settings the answer? I play Gibson Les Pauls with paf pickups. I still use the plexi's however at home I play THD univalve through a single 25w Celestian Greenback. The THD is uniformly biased to take any tube. I use a singel el34 and 12ay7's in the preamp and phase inverter. It is 15w
I can get huge amounts of sustain using just a Keeley Compressor and what is basically an 808 Tube Screamer by another name (it's a Maxon with the same chip). It definitely doesn't sound or feel like a cranked Plexi. As the other answer points out, nothing will re-create that. But you can get a different long-lasting violin-like sustain tone, even at lower volumes.
Regardless of chasing any particular tone, I can't imagine my board without a great-sounding compressor on it. I do feel like a compressor shines more with single coil pickups than double - or you can drop the volume control on the Les Paul a little bit to hit a compressor less hard. Sounds counter-intuitive but the pedals I have overcompress a bit with higher output pickups at full volume.
Big picture: I started trying to get great low-volume tone back in 1999. The best I have been able to do is use a low power tube amp and go for a different great tone from the high-volume tone(s) I use at gigs. That means I have to have high volume practices (ideally with the band) in order to fully prepare for gigs. That's true not just for the tone, but also for the fitting into the band sound properly and having the right levels for each part of each song. When I'm gigging hard, I have two pedalboards - one for home and one for high-volume, because even the same pedal settings sound terrible at home when they work loud, or vice-versa.
In all honesty, you won't get a tone all too similar at a reasonable to what you get from your Plexi at maxed volumed. A lot of that sustain and compression/sag comes from the power amp tubes being pushed hard, the speakers moving a lot (as well as having been broken in) and also having a tube in the rectifier position.
You can get a reasonable tone using a compressor but you'll really have to work on this and really tweak the settings down to a fine tuning. You'll also probably end up spending a lot of money on compressor pedals too, especially tube ones.
If you have a look at some TC Electronic compressors, find one that's got the Tone Print options and have a look into that, it should give you a little more control over your sound.