I've run my Jeeps forever with that set up in the rear. You may have a little issue with the rear trackbar touching the gas tank skid, but it can be clearanced a bit. A better option is to add an adapter to relocate the track bar. I have the one from JKS that moves the track bar up and forward a bit, so it relieves a little stress on the bushings created when you rotate the rear axle to point the pinion up. I also had to add brackets to move the rear shocks out a bit to keep the shock bodies from contacting the rear spring perches. I'm not sure that adjustable lowers would alleviate any of these issues, as I just don't have any significant experience with them. I've always run fixed lowers. Either stock or aftermarket.
For the fronts, the adjustables may be a good idea to try at 4". I had one early TJ with the Dana 30 and I was able to run fixed arms all the way up to 5" and had enough adjustment in the front with the standard cam bolts, to keep it going down the road well. However, on my newer TJR, I was fighting death wobble after installing OEM arms on it. Then I noticed the aftermarket fixed arms that originally came with the Jeep when I bought it (Superlift) were slightly longer than the stock arms, so I put them back on and it helped, although I was replacing a lot of parts around the same time. This is why I say it might be good to have some additional adjustment up front. Best bet is to just try it all out, but I think the rear should be fine running adjustables on top only. It will be interesting to hear what you come up with.