My untested opinion is that yes, if they are both DDR3 then the BIOS will run them at the slower speed and possibly worse timings to get them to work together. But is the second stick that you are looking at standard DDR3 ram? The standard stuff is used in desktops; notebooks usually use much smaller sticks and the form is not yet compatible across all; different makes or even models may take different ram. So is the second stick that you are looking at actually physically compatible with that machine?
There are many factors involved in RAM compatibility even if they're physically compatible with the system. Are they the same voltage, timings, etc. Even if they're 100% identical except for the clock speed difference, they might STILL not work together. RAM is finicky like that. Suffice to say that it's not very likely to work even if the modules are physically the same.
Now- sometimes, it will work by forcing all modules in the system to the lowest frequency/highest timings and whatever voltage they happen to agree on. However, oftentimes two different memory kits just don't work. Memory is sold in kits for a reason. The modules in a kit are tested to work together. There is never a guarantee of them working together with other kits even of the same model.