Welcome to the SMF family, slowandlow!
If I recall, this has been a mildly debated topic in the past, although I don't remember the threads or posters...probably buried in archives by now. And yes, not many brine their butts...here's where I stand on it, and how I got my opinion...by trials:
If you want to brine, you'll get the best results with previously non-enhanced butts (not cryo-vac packed). I've brined cro-vac packed butts before I tried fresh, and there was a very noticeable difference in benefit, so if you can get fresh, that's what you want to run with. If the butts are already in a solution, you won't do them much good with a brine due to having to use much higher salt concentration in the brine to overcome equilibrium of the meat's salt content from the existing solution it soaked in.
The major benefit to brining fresh butts vs just smoking cry-vac packed is that you can add the flavors you want to the meat through the brine solution you soak them in, and when done correctly there will be hints of your spices in the interior of the meat. You can then further enhance those flavors with your dry rub blend and choice of smoke wood.
Here's how I did a few smaller batches of butts (2 for each trial) in the past, with a salt/spice brine, no cure additives used:
Round one, 2-day brine of previously non-enhanced butts, with resulting smoke and review:
Round two, 8-day brine, otherwise, the same similar to the above, with better results:
Use the recipes if you like (we love this stuff), but the main things to consider are the salt content in the solution and the time allowed for brining.
The 8-day was a far better outcome with the finished products, while the shorter brine time did not penetrate completely throughout the meat, and the taste and texture was proof of my efforts.
I would have to say that if you used the same concentration of salt as my recipe calls for, 4 days may be a bit on the short side for full penetration through the average weight of butt (7-8lbs each). 6 days would likely take it the full distance and be right there where my 8-day brine was (the 8-day was a bit longer than needed, but no harm done, IMHO).
There may be a limited few others here who have brined some butts also, and can offer additional advice, but like Scarbelly and Chef Jimmy J mentioned, I haven't seen a lot posted about it here on SMF. There were a few who posted that they wanted to try it after seeing what I did with mine, but I haven't seen or heard anything about it since then.
Oh, concerning time to reach finished temps of 200+*, I have had average-weight butts run over 24 hours (25.5 is my longest, if I recall correctly) if I didn't pan and foil-tent or wrap in foil once they reached ~180* I/T where many will foil at. No-foil smoke produces a superb bark on the meat (depending on rub ingredients and how heavily it is applied) at the expense of very long smoking times, while foiling has reduced overall time in the smoker by approx 15-25%+, in my own experiences, depending on ambient humidity and other weather conditions, smoker type/manufacturer and mods, added humidity with water pans, chamber temps and ventilation rates, and last but certainly not least, the precooked weight of the pork butt.
Brining does bulk up the meat somewhat, as my trial runs indicated a considerable loss of liquid in the brine bucket when I pulled them out to rub and smoke. I don't recall if I ever took weights of the fresh vs brined to compare them or not, but volumes of brine were much less than I started with. The liquids get cooked out (in the form of water vapor) as part of the normal process of cooking, but I did notice a somewhat moister finished product compared to other basic prep methods I've used with cryo-vac packed pork, or fresh non-enhanced. I've brined butts, loin back ribs, whole pork loins, chops...can't think if there's any other cuts of pork that I've brined, but they all have benefited from it with added flavor and a bit more moisture in the finished products.
As for rubbing and wrapping to rest in the fridge, you may not want to go much over 8-10 hours if it's brined...maybe not even that long. The brine may begin to seep out of the meat while it rests (remember the process of equilibrium with salt, and the meat is now bulked up with salt-water) and turn your dry rub into a soup, and eventually start leaking out of the plastic wrap (definitely place wrapped meat in pans)...I've never processed 'em that way before, so I'm speculating here. I went straight from the brine to a rinse with mine, drip-dry, dry rub with NO SALT in the seasoning blend (brine adds enough salt), rested for a few minutes in a pan or on a board while firing the smoker, and went straight to the grates from there. If you're wanting to rest with a rub and wrap in the fridge for building the start of your bark, just be cautious on not going too long in the rub/wrap before the smoke.
Uh, I guess I didn't really say one way or the other where I stand on brining butts (the above links/threads should have covered it, though). I will say that if you have the time to get everything ready long enough in advance, can commit the fridge space and are willing to put in a bit of extra time to do the brine prep, there are benefits for the taking. With a well planned and executed brining project (don't jump the gun and pull from the brine too early, or botch-up a recipe regarding salt concentration), the benefits will be best. You don't want to just fumble through it and expect good results...that's setting yourself up for disappointment. Do the benefits out-weight that little bit of extra prep time, equipment (food-grade brining buckets) and fridge space? If you do it once and you do it correctly, you'll likely be back at it soon thereafter. It was not long after my first trial with brined pork butts when I was at it again (a week?...though I had previous experience with brining pork, just not fresh butts), so yes, I say it works, and when I want to take my butts a few notches higher than the average smoke, I go brined with a no-foil smoke. Again, referring to the third paragraph...it's all about the additional flavors, with a hint of better moisture content when the smoke clears.
Roll with it and make it happen! BTW, brining butts isn't difficult, it just requires a bit more patience then you may be accustomed to mustering up.
And, in case you're wonder by now, 3 average-weight butts (approx 23-24lbs total weight) should fit into a 5-gal bucket with some thought on positioning (definitely in a 6-gal without any problem) along with the brine needed to cover them up. 2 in a 5-gal has tons of space...just so ya know.