Can I use Google Emoji on mac? I want to use Google/Android emoji (noto font) instead of the standard apple emoji set. Can I do that on mac? 

sudo cp Downloads/NotoColorEmoji-unhinted/NotoColorEmoji.ttf /library/fonts/Apple\ Color\ Emoji.ttf doesn't change anything and SIP prevents changes to /System/Library/Fonts/Apple Color Emoji.ttf

I'm running 10.11.6 on a 5k iMac if it makes a difference
Yes, you can!
--EDIT--
The below still works, BUT, turns out, JoyPixels (open source emoji and the closest Google emoji / Noto Font replacement) has multiple versions of their emoji set including a .ttc file directly for download on their website for free that you can simply download and install as a font easily: https://www.joypixels.com/fonts
Fonts are in a .ttf file format, but Apple compiles those files using a SBIX format and others use other methods, typically CBDT/CBLC is used. Because of this, even though you have a .ttf file, it has to be compiled in the SBIX format. There is a user (vXBaKeRXv) on Github who has compiled multiple emoji fonts using the SBIX format. There's a Github thread and a Medium article on what to do. Quoting from the Medium article:

The Step-by-Step

Head over to this Github repo and download the .deb archive that contains your emoji set of choice.
Extract/open the .deb archive. Once inside, extract the archive named data.tar.gz. You’ll now see a folder called var. Inside that is a folder called mobile. Keep on going deeper and you’ll eventually reach your destination: a font file named AppleColorEmoji@2x.ttf.
Rename AppleColorEmoji@2x.ttf by putting spaces between each word and removing the ending, so that the new file name is Apple Color Emoji.ttf.
Keeping that Finder window open, start up Font Book (the built-in app where you can manage all the fonts installed on your device). In the left side panel at the top, select the ‘Computer’ option to show all the fonts you’ve installed as well as the default system fonts. If you scroll down the list of fonts, you should see an entry called Apple Color Emoji close to the bottom. This is the font file you’ll be overwriting, but don’t worry, this process is easily reversible!
Drag the Apple Color Emoji.ttf from the Finder window into Font Book. You’ll be prompted to install the font. It may warn you about it being a duplicate, but we already know that, so keep on going. Once you finish installing the new emoji font, you’re good to go! Try out your new emoji set by opening up your browser of choice, selecting a text field, and press CTRL+CMD+SPACEBAR to quickly bring up the emoji picker.


For step 2, this works on a Mac to unpack a .deb file without installing it:
ar -x path/to/deb/file.deb