The short answer is, no. You can't get necessarily get elementary OS versions of packages faster than they are released.
Selected packages for eOS are designed to be stable, and as such, if you want packages before release on eOS, you might need to be prepared to use unsupported packages, and they may or may not work as intended (although often you will be successful).
Using the command line, you can add the staging PPA, although this is not considered stable, so remember, this will add potentially unstable gnome3 packages as listed here.
If you are still willing to proceed you can then do this:
sudo add-apt-repository ppa:gnome3-team/gnome3-staging
sudo apt-get update
sudo apt-get upgrade
Of course you should take a backup first, and also - apps in the staging ppa will be moved into the main repository eventually.
If you have problems you can try downgrading again:
sudo apt-get install evolution=220.127.116.11
You migt need to double check the version number, but that is how you would install a specific version (which can be used to downgrade).
Let us know if you do try it, and if you encounter any issues, as nobody can ensure it will definitely work fully, without trying it, and I don't personally use evolution to check for you.
If you have not installed a custom PPA before, checkout this previous question / answer for help How can I add a PPA in Loki?