I would strongly advice against. Consulting Practical Programming for Strength Training, one learns that the optimal recovery time for a single muscle group is somewhere between 24 and 72 hours. Go below that and you can't fully utilize your full potential plus you risk overtraining and injury. Go longer and the training effect starts vanishing. Doing every muscle group only once a week thus is a huge waste of potential, which absolutely outweights the benefit of the higher training volume individual muscle groups receive due to the split (if there is a benefit to begin with, mind you).
I think nothing beats a full body routine when you're a novice/intermediate lifter and can train no more than three times a week, so I consider Starting Strength (novice) or the Texas Method (intermediate) a good starting point for pretty much anyone.
However, if you're set on your PPL split, I'd still recommend a consolidation of the routine, for example like this:
Day 1: Push & Legs
Day 2: Pull
Day 3: Push & Legs
Day 1: Pull & Legs
Day 2: Push
Day 3: Pull & Legs
You alternate those two weeks. That way, ample recovery time is ensured while every group is activated at least every four days. You likely need to ditch some of the suggested exercises. I would keep the big movements and dismiss the smaller isolation exercises (e.g. keep the narrow-grip benchpress and romanian deadlifts, ditch the triceps extensions and hyperextensions).
Final note: This answer asumes that you're not an enhanced lifter. With the use of steroids, C. Langes answer becomes much more feasible as, among other side effects, your body's response to training stimuli is prolonged.