As long as they specs match the RAM already in there it shouldn't be too much of a problem. That's not to say you can't put in mismatched RAM and not have it work. It just might run at less-than-efficient pace.
And even if the specs match, there's always a chance the motherboard won't like it and refuse to boot.
In summary, it's a crapshoot, but I think it'll be ok if you mix.
And worse comes to worse, you can just remove the 4GB already in there and have 16GB of RAM (which is more than enough).