Yes, it is drained and covered (except for the windows). The bad part is that for the entire week we saw no one working on it, and we passed it several times a day.
The other sad thing was that the amount of trash in and around the Trevi fountain was huge. There were a lot of school groups around, but there are no trash cans. We saw people just leaving their trash on the stone bench. Shame on them.
While I'm shaming.... shame on the Japanese tour group that would not stop using their flash in the Vatican Museum and double-shame on them for posing in the confessionals for pictures at St. Peters Basilica. My pet peeve is people, no matter their religion, not respecting others' places of worship.

Security took me well over an hour in August.

If you can afford it - take a taxi - I had amazing taxi drivers who not only took me to exactly where I wanted to go - but gave me commentary to boot! With some great English - not really but they certainly tried. I would do a drive by the Colosseum - very impressive and make my way to Piazza Navona and then soak up the culture with an expresso!
As for the Trevi fountain - worth a look - and it was clean in August.

I am of the opinion that a 6-hour layover is not a lot of time, especially for someone who is not familiar with the airport or city. It will take at least an hour and a half (likely two hours) to get from your seat in the plane to either Termini (Leo-Express) or Trastevere (FR1). You have to deplane, get through immigration, find/walk to the station, buy the tickets, and wait for the next departure before you even leave the airport. If you've never done it before, it can take some time.

Add an hour to get back (waiting for the next train, getting to security), and (conservatively) another 1 hour to get through security and to your gate - and the plane boards a half-hour before departure -- that takes another 2.5 hours off your time.

You now have less than 2 hours to see something...and you are still at the train station. My thoughts - one of these:

(a) LE train to termini. I like the Metro to Coloseo - quick look and walk in the forum to the Campidoglio...but I would not do much more than that. Then take the #40 bus back to Termini, it's termination stop. (NOTE: The #64 bus goes there too, but it stops more often.)

(b) FR1 train to Roma Trastevere and #8 tram toward Argentina. Get off right before the river. Xerox a walking tour of Trastevere from a guidebook before you leave home and do it for about an hour. Then take the #8 tram back to the station. (NOTE: When you exit Roma Trastevere station, walk straight ahead to the tram stop and take the tram that his coming from the left and heading toward the right -- it will say "Argentina" on the front.)

SS

My experience at the airport in Rome is that everything takes a very long time and there are lines. Leave yourself plenty of time for check in and going through security. It's very sticky there.

That said, and I assume you have never been there before----it's just such a friggin' mind blow of a beautiful city. My first taxi ride into Rome brought tears. I would take a taxi---yes it will cost a bunch but it will be worth it--it's Rome. Tell the driver what you are doing. Romans are proud of their city. Hopefully he will have a heart and take you past the ancient walls and drive you past the ancient sites. I really think that's all you have time for. I agree that the Basilica di Santa Maria in Trastevere is beautiful and worth seeing but if it were me and I only had one chance I'd want to see the architecture of Piazza San Pietro but that's just me. Good luck. I'm already nervous for you!