I don't think that you will have a problem at Kephart unless it is a holiday weekend. Icewater Springs and LeConte are prone to have people show up that are unaware they need to reserve a spot. A ranger will make sure you get your spot if there was one around, which 99.99% of the time there isn't. Getting there early also helps when securing a spot.
Whether you take a tent or not is up to you, but depending on when you are going, it probably wont be necessary. The ironic thing is, if you have a reservation and it is full (by someone who says they have a reservation and they don't) and you tent, you can be fined for it, which is wrong. Don't worry though, your odds of seeing a ranger are like being struck by lightning.
Kephart was redone in 2005 and the bear fence was removed and a porch added. It has built in benches and table, as well as a cooking platform on the side. It has a double deck sleeping platform which I always prefer the top. Sleep head out as the mice tent to run along the back wall of the shelters. I would rather them run over my feet as my face. Hang your food on the bear cables, don't leave crumbs, and either hang your pack on the bear cables, or on the strings in the shelter. Open up all of the zippers and what not on your pack so a mouse could get in and out without chewing his way in, which they will do. (personally, I have seen plenty of mice at shelters, but have never had them bother me or any of my stuff, but it does happen sometimes). Take earplugs as someone will snore.
Here is a list of the shelters in order of usage in 2008. As you can see Kephart is near the bottom. This does not include thru-hiker use.
Icewater Springs: 2651
Cosby Knob: 2003
Mt. LeConte: 1831 – Not on the AT
Pecks Corner: 1821
Tricorner Knob 1750
Spence Field: 1673
Derrick Knob: 1665
Silers Bald: 1564
Double Springs: 1447
Mollies Ridge: 1369
Mt Collins: 1345
Kephart: 1198 – Not on the AT
Davenport Gap: 987
Laurel Gap: 891 – Benton MacKaye Trail
Russell Field: 863