That should work pretty well I think. Again, others who are more experienced may have better advice but what I told you is what worked very well for me. It also wouldn't hurt to throw in Reverse Hypers on a leg day if you can just to keep the low back healthy.
As far as the belt goes: I had a low back injury (involving a stress fractured vertebrae and my disc @ L4-L5) 4-5 years ago now and both before the injury and after the injury I was all about not using a belt so that my low back would stay as strong as the rest of my body.Buddies offered me their belt to use sometimes, but I refused to even try it because I wanted that "raw" strength. Let me tell you, bad decision. I got the Rehband belt (a little expensive, but awesome) about a year ago now and it has helped my lower back health quite a bit. I tend not use it too much when I'm going light, but I use it on almost all my heavy lifts. I would actually say that my lower back is much stronger than ever now, thank God.
Just as an example of how (if used properly) it should help your lower back's raw strength: I remember reading an article by Andy Bolton (1000lb+ deadlifter), and if I recall correctly he used a weight belt on all deadlift sets that were over 1/3 of his 1RM. He also had never had a back injury, as far as I know. So, I think his back strength and back health speaks to the importance of a belt.
If your back stays healthy, it can keep getting stronger! Can't argue with that haha.
Alright, stay well and good luck!
P.S. Sorry for the long-winded response. In short, your program addition should work well.
EDIT: As far as muscular development goes: I don't think using the belt will be an issue, as long as you don't over-use the belt. Additionally, you still have isolation exercises if you are very worried about that.