Of course you can use the SSTRAN with a 102" CB antenna. How well it will work will depend on a number of factors.
First, the kit ships with no antenna connector because the FCC does not allow it. However, you as the kit builder may install any kind of connector you want. As long as your operation complies with Part 15 regulations, it does not matter.
If you directly connect the 102" CB antenna to the output of the SSTRAN, it will work exactly the same as a wire of the same length. With a typical setup inside your house, it will cover the house and out into the surrounding yard but not much more. That is because the matching network inside the transmitter, although it can tune over a wide range, is not very efficient. And also because the transmitter will not have an efficient ground system to work against.
If you follow the procedure in the kit manual and short out the internal inductors and use an external loading coil of the kind Carl sells, it will work much better. This is mainly due to the fact that the external coil is much more efficient. But it is also due to the fact that the coil will be tuning with the antenna capacitance only, and you will not use any auxiliary loading capacitance as you would if you used the internal matching network. The auxiliary capacitance in the internal network makes it easy to tune the transmitter, but you are shunting signal to ground that could otherwise contribute to useful range.
If you want to obtain the best range, you need to mount the transmitter outdoors over an effective ground system. In most cases, that means installing radial wires on the surface of the ground. Elevated mounting is not recommended unless you have a large metal surface that you can ground to, such as a metal roof. Beware of using a long ground wire; your system would likely be out of compliance with Part 15 rules in that case.