I did some research of my current back-up PC. The ram is DDR3 clocked at 1333MHz. I upgraded my ram a while ago, and it was clocked at 1600MHz. Did I do damage to my computer by having 2 different clock speeds? Does the 1600 bottleneck to 1333MHz? What happens when 2 ram modules have different speed?
Mixing memory is generally not advisable, but usually not very dangerous. The problem is that the PC you linked to doesn't support DDR3-1600 memory in the first place. So, even if you take out the 1333 it came with, it will either down-clock the 1600 to 1333, or may not work at all and give you a memory error when you start up the computer.
i checked the link you posted in the OP your mobo/cpu doesn't support higher than 1333 mhz. so even removing the 1333mhz stick your ram will still be capped to 1333 mhz
edit : if your running 8 gigs of ram the speeds are capped to 1066mhz