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
In order to upgrade to macOS High Sierra, you should be running at least OS X Mountain Lion. I suggest you upgrade to macOS Sierra first, which you can get here: Get macOS Sierra.
You can check here for more information on upgrading to macOS Sierra: How to download macOS Sierra
You may need to reset your Mac's software update URL. You can follow the guide at Robin's Blog to learn more about this. This excerpt from the post explains how to reset the update URL;
- Open the /Library/Preferences folder on the main hard drive.
- Find the com.apple.SoftwareUpdate.plist file and move this to the desktop (the easiest way is just to drag and drop the file to the Desktop). If you find a similar file with a .apple at the end (com.apple.SoftwareUpdate.plist.apple) then move that too. Moving them to the desktop means that you can restore them if this goes wrong.
Best Answer
If your drive is formatted with HFS+ and not APFS, you may be able to use DiskWarrior to repair your drive enough to use Target Disk Mode to extract your data through another Mac onto another disk. However, if the magnet damaged the partition table, or primary and alternate volume headers, or too much of the catalog & extents files, DiskWarrior may not be able to help. In that case you may have to use a professional recovery service like DriveSavers or face the music and start over.
In any of the above situations, once you've gotten your data recovered (or decided not to), you will need to do a full erase & install of macOS. You can do this by creating a bootable installer on another Mac.