Yes.You can install and use 16GB of RAM in that machine. There are several discussions in Apple's forum on this subject.
I Have same same model MBP and upgraded two weeks ago. Works great.
Edit: (as to the comments)
This is the product I have purchased to my mac. Please, before you buy make sure that the memory fit your specific mac model. Apple do have a good webpage of How to identify my mac model.
Here, you can find a similar discussion in iFixit forum
In my original answer I have mentioned SSD. Thanks to @tubedogg clarification, the SSD and RAM are unrelated in this discussion. Yet, when upgrading considering to upgrade the SSD is not a bad idea.
Sorry for the bad analogy: it is like replacing parts in your car that will make it runs great, but it takes 15 minutes to start it.
For me, I decided to start with RAM. Upgrading the Hard Drive, made it even better.
I didn't see the Mac going over 8MB yet, so I opened every application on my mac just to get to 51%. Since the update it usually runs between 30%-45% of RAM used.
Which brings me to the following conclusion:
- Can You install 16MB RAM? Yes
- Do you need it? depends on your usage
- Why would you still install it? Upgrade once, even if you don't use it right away
- Should you also upgrade your hard drive? If you have the resources (money, time, transfer method), then yes