I don't think it is a good thing to do at the moment because I am pretty sure that something broke JACK realtime support a while back and I haven't quite figured out what yet. But apart from this it probably could be done, I don't know exactly how well it would work as it isn't something that I have put in much effort into trying. I just use JACK to the side of PulseAudio for audio production workflows like piping sound from a synth plugin to other plugins, then to the DAW (Digital Audio Workstation) and then out to my speakers. However, I do have some notes that I have found while trying to use JACK more in day to day usage.
One major issue that you might encounter is that our firefox build doesn't support JACK (might be worth enabling in the future though) which means that you get no sound if you cleanly rip out PulseAudio. To get sound from it (or any other software without JACK support for that matter), you would need to use a converter between between the two audio backends. This can relatively easily be done by using Cadence (I am working on soon getting it into the repo) and then installing pulseaudio-module-jack
from the repository. Please note that in my little test session with using it in cadence, it totally messed up my regular PulseAudio setup when not using JACK, so there might be some commitment here to do. I won't take any responsibility if you need to reinstall (like I had to do) to get audio back when not using JACK and the converter. You will also need to, for most applications, need to manually wire every program to the output using software like Cadence or Qjackctl (in the repository).
The short answer really is no, but maybe at the moment. It could work and be very useful because you could pipe all your sound through an equalizer before sending the equalizer output to the speakers. However, at the moment I think you would be relying on conversion programs that may or may not mess with the regular default PulseAudio setup. The piping of sound is great when you need to pipe audio between stuff, but might get in the way of normal day to day usage. There are people out there that are way better with using JACK than I am so they might have much better tips and tricks to using it, but this is my opinion of the situation.