Yes, a 1600MHz single stick of RAM will still run at 1600Mhz if it is installed alone.
Dual channel doesn't split the frequency of the RAM module in half.
Further reading if you are interested:
Here is an article explaining how Dual Channel Architecture works: http://www.hardwaresecrets.com/everything-you-need-to-know-about-the-dual-triple-and-quad-channel-memory-architectures/
Here is a good article explaining RAM timings and frequency: http://www.hardwaresecrets.com/understanding-ram-timings/