I think this could be a really good split, if approached properly. It's actually similar to what I do and I like it.
Your split days should be heavy and high volume, whereas you full body day should be lighter weight and lower volume per lift.
Chest day - maybe on chest day your doing 4 sets of flat bench 4 sets of incline and some dumbbell work, with heavy weight about 8-12 reps. Thats going to be your high volume day. Similar for leg and back, more sets and high intensity.
Full body day - I would do a single compound movement for each body part, and only do about 3-4 sets (probably still 8-12 reps). This gives you the opportunity to hit each body part twice a week, which is often recommended. Your full body day will have about the same volume and intensity as your split days, just spread out over the whole body. Just be smart about the exercises you pick and the order. e.g. deadlifts exhaust my lower back so I wouldn't do deadlifts and squats back to back, maybe deads, bench, pulldowns, squat...
If you could do 6 days a week, then just doing another round of your body part splits could work, but you could also get some unique benefits from this full body day. There is nothing inherently bad with the plan you proposed, just use common sense, don't overtax your body on that friday, if your splits have left you too tired. Depending on you body you may need to switch up the order (e.g. I would do legs on Monday, because if I did legs on Wed. they would still be shot by Friday).
Some other benefits.
- You probably have more time on Friday to hit the full body workout. It will most likely take more time.
- The gym is probably more empty on Friday so you'll be able to switch between equipment more easily.