I tested Mint MATE 18 and the main menu had the search and quick launch feature working with MATE Desktop 1.14.1.
I just upgraded my Ubuntu MATE 16.04.1 to ver. 1.14.1 of MATE Desktop with mate-menu 5.7.1-1 and there is no main menu quick launcher. How can I get quick launcher working?
The quick launcher can be enabled in MATE Tweak (which is part of the default installation):
Click Interface and then check the box Enable Launcher
You will see the launcher icon appear in your indicator panel:
And when you click it you get this dialog to search:
Actually I have the same issue using ubuntu 16.04LTS with MATE 1.16, you can install mate-menu and add it but there is a bug and every time you start it a bad error appears (already opened issue on https://bitbucket.org/ubuntu-mate/mate-menu)
Instead using ubuntu 16.10 with mate 1.16 mate menu works correctly and you can also add brisk menu https://github.com/solus-project/brisk-menu (not compatible with 16.04 version)