Absolutely. I rinse thoroughly immediately after pouring the beer, put the bottles away until next time. Then I sanitize with Star San using a vinator, and re-bottle.
This had been my exact system for the past year or so, but I was not sure the bottles were really "like new" by the time I was refilling them. I made the decision for my last batch that while I had a bucket full of hot PBW from cleaning the bottling gear, I would carry my two cases of bottles inside and give each one a good shake full of PBW and make a close inspection before rinsing and sending on their way to the vinator full of Star-San.
I am so careful about sanitation pre-fermentation, it seemed a little silly to skip a 30 minute step on bottling day and break the rule; first clean, then sanitize. You will always clean your carboy with PBW before rinsing and adding Star-San, so why not give your bottles the same respect? You already invested 6 hours on brewday, and 4 weeks for fermentation, so why not spend an extra 30 minutes on bottling day and treat those bottles right.
So.....
Drink, hot water rinse, semi-clean storage, (then on bottling day) clean with hot PBW, hot water rinse, Star-san, bottle tree, fill.
It seems so obvious, I don't know why it took me so long to start doing it. Also, I am going to make a bold statement - no homebrewer has regretted purchasing a bottle tree or Vinator. They make things so much smoother.
Joe