I've been doing it for almost a year and haven't had any issues. In fact, I would argue that when I felt fatigue/nagging issues when doing my deadlifts after my squats, it indicated to me that I was probably having some issues with my form on my squats.
The issue I ran into was fatigue with trying to deadlift twice a week - once the program switched to squats 3x/week and deadlift 1x/week, I've been fine. Though the squats are "easy" on the same day as deadlifts now, whereas before I was pushing for maxes in both on the same day.
I have probably used a leg press 5 times in my life so no help there. If I was trying to build size in my legs, I might add them as an accessory but don't think I could ever abandon squats entirely.