Okay, I pulled this up on Google in its entirety, and unfortunately the page was skipping up and down as I tried to scroll through. The best I am able to gather here is that Thoreau is citing the morning and time of waking (more than the time of day), as a specific time for self renewal. Bathing is a cleansing ritual, and it is also a relaxed time during which a person can allow themselves the time to reflect, imagine, think, and cleanse their mind as well as their body.
He also cites this spiritual and physical bathing as a prerequisite to preparing the mind (or brain) for "effective intellectual exertion," which can only be attained after proper rest and appropriate preparation (clearing the cobwebs, if you will). A carpenter can perform his job without this, his work is different, it's learned............. an intellectual is always learning, and therefore has to begin each day with a pure and open mind.
Finally, yes, I think it is possible to become "renewed." As a teacher, I can tell you that it's difficult to approach a new day in the classroom if you're still mulling over what didn't necessarily work well the day before. A student never performs to the best of their ability when they're worrying about yesterday's test grade rather than soaking in the new information they're presented with the next day. Students, as well as teachers, purify and renew themselves during scheduled breaks in the school year, and it's integral that they take the time to knowingly renew themselves in order to better prepare for their return to the classroom.
I hope this gives you a better perspective.............. I think I need to renew myself after the night's rest! :-D