"Is one full day long enough to get to the Center Basin for Roads End?"
Only you can answer that.
As I stated, it is about 14 miles from Roads End to the trail junction at the bottom of Center Basin, plus it is about 5700 feet of elevation gain. That doesn't get up up into the Center Basin.
At the last time that I left Roads End, I managed to get out 14+ miles and 5000 feet up to Lake Reflection, and that was by 3 p.m. However, I had started at 6 a.m. while it was cool, I was going solo, and my pack weight was tolerable. Also, I was trying to beat the afternoon rain storm.
Besides, for some people, 5000 feet or 10,000 feet are high enough that they can feel it, and they get slowed down. For others, a day or two of acclimatization will help a lot.